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MAPS AND SURVEY 



CAMBRIDGE UNIVERSITY PRESS. 

ILonion: FETTER LANE, E.G. 

C. F. CLAY, Manager 



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MAPS AND SURVEY 



A BY 

ARTHUR RFHINKS, M.A., F.R.S. 

CHIEF ASSISTANT AT THE CAMBRIDGE OBSERVATORY 
AND UNIVERSITY LECTURER IN SURVEYING AND CARTOGRAPHY 



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Cambridge : 

at the University Press 

1913 



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Camfirtirgc : 

PRINTED BY JOHN CLAY, M.A. 
AT THE UNIVERSITY PRESS 



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PREFACE 

'nr^HIS book is designed as an introduction to the study of 
•^ Maps and the processes of Survey by which they are 
made. 

In planning the work it was necessary to decide in the first 
place whether to call it Maps and Survey, or Survey and Maps : 
that is to say, whether to take the logical order, of Survey 
before Maps, or the order of general interest and use, which is 
Maps before Survey. 

Since many more people use maps than are engaged in 
making them, or than need to know the details of how they are 
made, it seemed better to begin with the consideration of the 
map as it is published and used. A clear understanding of the 
best results that have been produced up to the present time, 
leading to an appreciation of the ways along which progress is 
desirable, will make a convenient basis for the study of the 
methods of Survey, and the manner in which our representation 
of the world's surface may be extended and improved. 

Some years of experience in teaching the elements of 
Geodesy and of Topographical Survey to the students of the 
Department of Geography in the University of Cambridge 
have shown me that there is need of a book which shall give 
a general account of the many-sided art of Survey. The two 
official military textbooks, the Textbook of Topographical Sur- 
veying, by Colonel C. F. Close, and the Manual of Map Reading 
and Field Sketching, are invaluable for instruction in all the 



vi PREFACE 

details of the various processes, and there is no need to make 
any attempt to replace them. But it seems to me that the 
student needs some explanatory introduction, unobscured by 
much detail, which shall exhibit the general nature of the 
operations, and the relations to one another of the various parts 
of the subject. 

It is certain, also, that the student of geography requires an 
elementary account of the operations of Geodesy proper, that 
is to say, of the higher survey whose aim is to contribute to the 
knowledge of the size and shape of the Earth ; and which has 
in recent years extended its enquiries into the constitution of 
the Earth's interior. These subjects are entirely excluded from 
the official books mentioned above, and I do not think that 
there is any book which gives a general account of this most 
interesting part of the subject. 

The ultimate refinements of Geodesy cannot affect the maps 
in the slightest degree, cannot be said to be of any practical use 
whatever, can offer no return in cash for the money which may 
be, and which ought to be, spent upon them. Their justification 
is on a higher plane. A nation is judged, and rightly judged, 
by the public spirit and the public taste which it shows in its 
buildings, its pictures, and its gardens, which any educated man 
is, or thinks he is, competent to appreciate. And equally a 
nation is judged, though by a smaller circle of judges, for the 
contributions which it can make to pure knowledge. An ex- 
quisite piece of Geodesy may give as real a pleasure, and be as 
genuine a source of pride, as the masterpieces of art and 
literature. 

I have made no attempt to describe the minutiae of instru- 
mental adjustments or processes, believing that a general view 
of the subject should not be obstructed by a mass of detail 
which is tedious to read, but had better be avoided until the 
student comes to deal with the instruments themselves, and 



PREFACE vii 

carry out an actual piece of survey with them. Nor have I 
been able to give anything more than the slightest sketch of the 
large subject of cadastral survey. This is an intricate subject 
whose methods are to a great extent governed by the system 
of land registration and taxation in force in the country to be 
surveyed. There is a recent treatise on the subject — The 
Cadastral Survey of Egypt, by Captain H. G. Lyons, F.R.S., 
Surveyor-General — to which students may be referred if they 
wish to find a lucid account of the most interesting problems 
involved in this class of survey. 

In the treatment of the topographical and geodetic survey 
I have tried to follow as closely as possible the principles under- 
lying the methods employed by the Ordnance Survey, the 
Survey of India, and the School of Military Engineering at 
Chatham, to whose hospitality I owe my first introduction to 
the subject. I have profited also by the publications of the 
Geodetic Survey of South Africa, the United States Coast and 
Geodetic Survey, and the Survey of Egypt. Part of the charm 
of Geodesy is due to the general compatibility of the ideas 
which govern the operations of all countries, which may be 
traced without doubt to the influence of the International 
Geodetic Association, and to the benevolent authority exer- 
cised by the illustrious Director of its central bureau at 
Potsdam. 

While the literature of Geodesy and Topographical Survey 
is extensive, comparatively little has been written on the subject 
of topographical representation on the map. The subject is 
new, because until the introduction of the present processes of 
colour printing there was not a great deal of scope for enter- 
prise. It is still in the experimental state, as is evident from 
the continual change in the style of the publications issued by 
the principal map reproduction offices. Under these circum- 
stances discussion and criticism are doubly interesting, and 



viii PRE FA CE 

I have devoted more space than might seem necessary at first 
sight, to the detailed analysis of typical sheets produced by the 
leading surveys of the World. But since it is impracticable to 
give adequate specimens of these maps, this analysis can be 
effective only if the student is able to study a selection of the 
actual sheets. For this reason I have given the sheet numbers 
of good specimens, in the hope that the schools of geography 
who may be interested in the subject may find little difficulty 
r in procuring a characteristic series of maps. 

By permission of the Controller of H.M. Stationery Office, 
and with the very kind assent and help of Colonel C. F. Close, 
C.M.G., R.E., Director-General of the Ordnance Survey, I am 
able to give in Plates I to V small specimens of the maps of 
the Ordnance Survey of Great Britain and Ireland. It is not 
possible to do justice to these maps in the small page of this 
book ; but I trust that these specimens are sufficient to show 
the high quality of the work of the Survey, and to serve as an 
incentive to the study of the complete sheets. I am especially 
indebted to Colonel Close for undertaking the complete pro- 
duction of these plates in the printing department of the 
Ordnance Survey at Southampton. 

Plates VI to IX I am able to give by the kindness of 
Colonel Hedley, R.E., Chief of the Geographical Section of 
the General Staff. He has been so good as to take great 
interest in the choice of specimens from the wide range of 
maps produced by his department ; and in particular he has 
kindly placed at my disposal a specimen of the new edition 
of the beautiful map of Persia and Afghanistan which is in 
course of preparation. These four plates have been printed 
in the map reproduction department of the War Office. I owe 
to Colonel Hedley my sincere thanks for thus making it possible 
to include in my book four attractive examples of small scale 
maps. 



PREFACE ix 

The material for the plates showing instruments and methods 
I owe to many sources. Commandant Lucien Durand, of the 
nth Regiment of Artillery of the French Army, was so kind 
as to give me the three pictures reproduced in Plate XVII, 
showing the reconnaissance ladder and beacon scaffold which 
he introduced into the equipment of the Service Geographique 
de I'Arme^e. To Captain E. M. Jack, R.E., British Commissioner 
in the survey and delimitation of the Uganda-Congo boundary, 
I owe the two pictures of beacons which make Plate XVIII, 
and the two pictures of base measurement on Plate XIX. The 
two latter were given me by Captain Jack to illustrate a paper 
read before the Research Department of the Royal Geographical 
Society, and the Society has kindly lent the blocks from which 
this plate is printed. 

The three figures of Plate XXI are taken from the Account 
of the Principal Triangulation of Great Britain, published by 
the Ordnance Survey, and those of Plate XXII from recent 
volumes of the Survey of India. The view of Banog mountain 
in Plate XXIII is from the same source. 

The diagrammatic figure of the plane table used by the 
United States Coast Survey is borrowed from one of their 
official publications, and the picture of the geodetic level on 
Plate XXIII was given me by Messrs E. R. Watts and Sons, 
who make this pattern. The remaining figures are from photo- 
graphs of instruments belonging to the Department of Geography 
of Cambridge University. 

A. R. H. 

Cambridge, 
May, 1913- 



CONTENTS 



CHAPTER I 

MAPS 










PAGE 


The necessity for Maps ....... 2 


Conventional signs 










5 


Roads ..... 










6 


Railways .... 










9 


Scale 










10 


Construction of scales for Maps 










13 


Problems in the construction of 


Scales 








14 


Rivers 










15 


Woods and forests 










17 


Sheet margins 










17 


Representation of hill features 










19 


Hachures .... 










20 


Hill-shading . . . -. 










21 


Spot heights .... 










23 


Contours and form lines 










23 


Layer colouring . 










27 


Combined systems 










29 


Map reading. 










30 


Sections and profiles . 










30 


Problems of intervisibility . 










32 


Identification of distant objects 










33 


Measurement of areas . 










33 


Measurement of distances . 










34 


Map reproduction 










35 


CHAPTER n 


MAP ANALYSIS 


Ordnance Survey Maps 37 


Maps of the General Staff . 










41 


Foreign Maps 










43 


International Map 










50 


Aero maps 










56 



XIV 



CONTENTS 





PAGE 


Precise traversing 


162 


The Ordnance Survey ...... 


. . 163 


India : Canada : Australia 


. . 167 


British Africa 


168 


Boundary Surveys ...... 


169 



CHAPTER VII 

GEODETIC SURVEY 



Figure of the Earth 

Deviations of the vertical 

Attraction of the Himalayas 

Gravity survey with the pendulum 

Gravity in India .... 

The theory of isostasy 

The form of the ocean surface . 

Geodetic measure of arc of meridian 

Principal geodetic arcs 

Geodetic triangulation . 

Principal chains . 

Geodetic bases 

Geodetic levelling. 

Future progress of geodesy 

Figure of the Earth 



171 
172 
173 
175 
176 
177 
178 
179 
iSi 

183 
184 
185 
187 
189 
191 



CHAPTER VIII 



SURVEY INSTRUMENTS 



The Sextant .... 








192 


The Theodolite 








194 


Levels ..... 






' 


196 


Invar wire apparatus . 








197 


Longitudes by telegraph 








197 


Longitudes by wireless 








198 


Geodetic pendulums 








200 



Index 



203 



PLATES 

To face page 

I. Conventional signs : One inch Ordnance Survey Map . 6 

1. Double and single railways. 

2. Mineral lines and canals. 

3. Roads of different classes. 

4. Footpaths and parish boundaries. 

5. Characteristic sheet attached to One inch map, O.S. 

II. Conventional signs, co7itimied ...... 10 

1. Hachures and cliff drawing. 

2. Confusion of contours with other detail. 

3. Correct method of figuring contours. 

4. Misleading effect of unequal vertical interval in 

contours. 

III. Conventional signs, coiitiniied 16 

1. Marsh. 

2. Sands. 

3. National boundary. 

4. Rock and water lines. 

IV. Ordnance Survey of England. One inch scale. 1/63360 24 

1. In outline, without hills. 

2. In colour. 

V. Ordnance Survey of Ireland. Half inch scale. 1/126720 28 

1. With hill shading. 

2. Layer system. 

VI. Geographical Section, General Staff. Basutoland. 1/250000 42 

VII. Geographical Section. General Staff. Persia and Afghani- 

stan. 1/4055040 43 

VIII. International Map. Sheet North K. 35 Istambul . . 54 

IX. International Map. Sheet South H. 34 Kenhardt . . 55 

X. Measurement of areas 58 

1. Amsler planimeter. 

2. Central parts of planimeter. 

XI. Determination of Heights ....... 74 

1. Aneroid barometer. 

2. Boiling point apparatus or hypsometer. 

XII. LeveUing 96 

1. Levelling staff. 

2. Twelve inch Y level. 

XIII. Compass sketching. The Service protractor . . . 102 

XIV. Instruments for compass sketching 104 

1. Prismatic compass, Mark VI. 

2. Compass in use. 

3. Compass in position for use. 

4. Clinometer in use. 

5. Watkin clinometer. 

6. Interior of clinometer. 



xvi PLA TES 

To face page 
XV. Instruments for plane-tabling . . . . . . 112 

1. Plane table and sight rule. 

2. Indian clinometer on plane table. 

XVI. Instruments for plane-tabling 120 

1. Trough compass. 

2. Plane table and telescopic alidade. 

XVII. Reconnaissance ladder and beacon: Commandant Durand 136 

1. Ladder on the march. 

2. Ladder in course of erection. 

3. Double tripod scaffold. 

XVIII. Uganda-Congo Boundary . . . . ' . . . 140 

1. Beacon for intersected point. 

2. Quadripod beacon for triangulation. 

XIX. Measurement of Semliki Base, Uganda-Congo Boundary 146 

1. Taking readings on the wire. 

2. Adjusting the straining trestles and wire. 

XX. Five inch Micrometer Theodolite . . . . . 150 

1. In position for triangulation. 

2. From the eyepiece end. 

3. With reflector over objective for lamp illumination. 

4. With electric illumination. 

XXI. Ordnance Survey: Principal triangulation. . . . 164 

1. Measurement of Lough Foyle Base. 

2. Great Theodolite. 

3. Scaffold on Gravelines Church. 

XXII. Survey of India ......... 176 

1. Half-second pendulums. 

2. Clock and flash box. 

3. Latitude with zenith telescope. 

XXIII. Precise levelling .188 

1. Banog mountain. 

2. Precise level: U.S.C.G. S. pattern. 

XXIV. Invar tape base apparatus ....... 197 

1. Straining trestle. 

2. Tape on drum. 

3. Mark on tripod. 

4. Alignment sight on tripod. 



CHAPTER I 

MAPS 

Topography means, in the original Greek, the description 
of a place, A map is a drawing to illustrate such a description. 
By gradual steps it has been found possible to make these 
drawings in such a way that they convey the necessary informa- 
tion without the description in words, and what is now called 
a topographical map can give, to those who know how to read 
it, all the information which is wanted to enable a man to judge 
of the natural obstacles which may hinder his getting about 
the country, or the means of communication which have been 
established by man to facilitate his journey. In this book we 
shall be concerned chiefly with these topographical maps. 

The amount of information which can be compressed into 
a map depends in the first place upon the perfection of the 
system of conventional signs in which the map is drawn, and 
secondly upon the size of the map in comparison with the ground 
which it represents, or, in other words, upon the scale of the 
map. It is clear that the larger the scale, the more detailed is 
the information which can be given. But, on the other hand, 
the larger the scale, the greater is the number of sheets required 
to cover a given area, and the more cumbrous is the map to use. 
For purposes of local administration and government it is 
necessary to have maps on which every separate property, how- 
ever small, is distinctly shown ; but such detail would be only 
confusing to those who wished to learn the way about the 
country. And again, the details of roads, the shapes of the 
hills, and all the other information essential to the traveller on 
foot or on wheels, are equally unessential to those who use the 
map for the study of broad questions of history, of commerce, or 
any such matters. 

H. M. S. T 



2 MAPS 

Hence we shall find that maps may be classed in three 
principal divisions : 

Cadastral maps, on large scales, show boundaries of property, 
and individual buildings. They are required for local administra- 
tion and taxation ; the management of estates ; the identification 
of property in legal documents ; and for detailed affairs of every 
kind. 

But it should be remarked that the English map on the scale of i in 
2500, commonly called the 25 inch map, shows the visible hedges and fences, 
whereas the real boundary of the property is very frequently some feet 
beyond the hedge. Hence the 25 inch map is not strictly a cadastral map, 
though it is commonly called so. 

Topographical maps show the natural features of the country, 
hills and rivers, forests and swamps ; and in addition such 
artificial features as man has added to the country in the shape 
of towns and villages ; roads, railways and canals ; bridges and 
telegraphs. They serve as guides for travel on business or 
pleasure, or for the operations of war. They are on smaller 
scales than the cadastral maps, and cannot show the boundaries 
of individual properties. The inch to the mile map is the 
standard topographical map of the British Isles. 

Atlas maps are on scales still smaller. Most of the topo- 
graphical details have been suppressed ; only the principal 
ranges of hills and the main streams of the rivers, the chief 
towns, and perhaps the main lines of the railways can be repre- 
sented, for they aim at representing on a single sheet a whole 
country, a continent, or even the World. 

The necessity for maps. 

It is a little hard for one who lives in a country long settled 
and completely mapped to realise the difficulties which confront 
at every turn those who find themselves citizens of a new and 
unmapped country. The need of maps appears most urgently 
in case of war, and in the past it has usually happened that 
military necessities first compelled the production of a map. 



MAPS 3 

The beginning of the Ordnance Survey of Great Britain may be 
traced, for example, to the Highland Rebellion of 1745. In 
peace the necessity of maps for all purposes of administration is 
less conspicuous, but none the less real. Until a country is 
mapped it is impossible to devise any well considered schemes 
of communication ; until it is surveyed on a fairly large scale 
it is impossible to make grants of land to settlers, or at least it 
is impossible to give them a clear and undisputed title to their 
holdings. In larger affairs the need of maps is equally great. 
Until a country is mapped it is impossible to agree upon a 
boundary which shall be satisfactory to both sides, and in the 
absence of maps the most costly mistakes have been made 
through sheer ignorance. 

Let us take two or three examples. 

During the war in South Africa the British army in Natal, 
advancing to the relief of Ladysmith, found the Boers entrenched 
in a strong position at Colenso, on the north bank of the River 
Tugela. On the right of the British was Langwane Hill, which 
appeared to lie to the north of the river, though in reality the 
river turned away sharply to the north, leaving the hill easily 
accessible to the British troops. Although the country had been 
settled for many years there were no maps in existence. 
Langwane Hill was the key to the position. The failure of the 
British commander to realise that it was accessible cost the 
country many hundreds of lives and weeks of prolonged fighting. 
The mistake could not have been made had the country been 
mapped. 

Again, until a country is mapped there is continual waste in 
making surveys for special purposes. If a railway is projected 
it is necessary to make a special survey of the proposed course 
of the line. This survey costs a large sum of money, but since 
it is made for a special purpose it is not complete ; it is never 
published, and cannot be made use of as a contribution to 
the proper mapping of the country. In the earlier part of the 
nineteenth century, while the Ordnance Survey was in the initial 
stages, several million pounds were spent in England on railway 
surveys, surveys for the commutation of tithe, enclosure of 



4 MAPS 

common lands, and so forth, nearly all of which money might 
have been saved had the regular survey of the country been 
finished earlier. It is the truest economy to push forward the 
survey of a country at the earliest possible moment. 

To take a somewhat different case : it is most important that 
the responsible officers of Government should be trained to 
discriminate between maps which are reliable and those which 
are not. It frequently happens that the first rough maps of 



\ 

o° 


L 
GEORGE 


j V / 





Scale of Miles 



Fig. I. True position of the 30th meridian, which was supposed 
to pass through the middle of the lake. 



a newly explored country are compiled from inaccurate observa- 
tions made under great difficulties by the early explorers. For 
example, the early maps of central Africa showed the thirtieth 
meridian passing through Lake Albert Edward, and on the 
partition of Africa in 1894 it was agreed that the boundary 
between Uganda and the Congo Free State should follow this 
meridian, so that both countries should have access to the lake. 
Some years afterwards it was found that the thirtieth meridian 
was actually some miles to the east of the lake. Prolonged 
negotiations were necessary for a rectification of the frontier, 



MAPS 5 

and some considerable sacrifice of territory was required to gain 
that advantage which the treaty was in the . first instance 
supposed to secure. This costly mistake would have been 
avoided had the diplomatists realised the necessary limitations 
of the maps which they were using. 

We need not spend more time in insisting on the importance 
of making maps, and of understanding how to use them. 

Conventional signs. 

In order that it may be possible to compress as much 
information as is required into the minimum of space, to ensure 
clearness and legibility, it is necessary to adopt a carefully 
considered scheme of conventions, so that the character of every 
line and the style of every letter may convey a definite meaning. 
The map thus becomes a kind of shorthand script, whose full 
meaning cannot be understood without a thorough knowledge 
of the system employed. It is therefore clearly advantageous 
that mapmakers should come as soon as possible to some general 
understanding on the subject of conventional signs, in order that 
it may not be necessary to learn, as it were, a new language 
whenever- one tries to read a new map. 

The resolutions of the International Map Committee, which 
met in London in 1909 to frame a scheme for the one-in-a- 
million map of the World, are in this respect of great importance, 
and we shall often refer to them in what follows. 

The characteristic sheet. 

The characteristic sheet is the key to the system of con- 
ventional signs employed on the map. It is usually, though not 
invariably the case, that each sheet of a map bears a small 
characteristic sheet of the principal conventions (see Plate I) ; 
but for a complete understanding of the system it is always 
necessary to refer to the complete characteristic sheet that is 
published separately. 

Conventional signs for use in the field. 

These are necessarily simpler and less minute than the signs 
which are employed on the engraved or carefully drawn sheets 



6 MAPS 

that are issued from the reproduction office. The surveyor in 
the field has neither the skill nor the time to imitate the finely 
devised style which is suitable for the engraved map. We must 
therefore be careful to distinguish between the systems to be 
employed in the two cases. (For a conventional sign sheet for 
field use, see the Manual of Map Reading and Field Sketching^ 

Roads. 

In reading the representation of roads on a map, it is 
necessary to remember first of all that the road is not represented 
true to scale in width, but that the width is conventional, 
signifying the class of the road. Such a convention is clearly 
necessary. On the scale of one inch to the mile a road sixteen 
yards broad would, if shown true to scale, be only one hundredth 
of an inch broad ; and this is far too little for legibility, or to 
allow distinctions between the representation of different classes 
of roads. Hence roads must be shown of a conventional width ; 
and when the scale of the map is doubled it is by no means 
necessary that the road shall be drawn twice as broad as before. 

There are considerable differences in the conventional signs 
for roads in use in different countries. We will examine three 
typical cases: the British Ordnance Survey; the French 1/50,000 
map published by the Service Geographique de I'Arme'e; and the 
1/1,000,000 International Map. 

Ordnance Survey. 1/63,360, or one inch to the mile. (See 
Plates I and IV.) 

A distinction is made between fenced and unfenced roads, 
the former being shown by double continuous lines, the latter 
by dotted lines. The distinction is of military importance, 
since fenced roads afford cover and obstruct the free passage of 
troops across country. Three grades of metalled roads are 
distinguished by differences in breadth, and the first two grades 
are coloured orange. Unmetalled roads or cart tracks are shown 
by still narrower double lines, and footpaths are long-dotted, 
but are with difficulty distinguished from parish boundaries, 
which are not needed on a topographical map. (See Plate I.) 

It is often found that the distinction made on the map 



CONVENTIONAL SIGNS PLATE I 

One Inch Ordnance Survey Map 




Double and Single Railways 




Mineral Lines and Canals 




% ^ :^ \ 



Vhnitt '^t?/" W/ -^ -^ ^ - <^ 




Roads of Different Classes 



Footpaths and Parish Boundaries 



\CetaUed Iijiad.9. First Class 

SecoTiA O^iss ft' 

Third Class I 

^nmetajted Roajis 

^ootpeiths ^ _ „ 



Twc 



5 CMUb distmice,' 



^faternl Lines and Tr 




CJiurch or- Chapel \*nth Tower' 

„ w-itJiout Tower' ot' Spire 

Windmtll ^ Wzn^pzmzp .. 

JOetterSooc 

Contozirs — -25°—' 

^oJtndarieSjCcmnty • - • - « 

TarisTi _ 

. ^„ {^ost Ome^ „ 

At ViUn<jes 



■dge Over £j}ldqf Undfr 



\l'o.9tS:^Teleefraph Office T. 



Rivers and Streams when e.Tcee-dzn^ IS feet in width are shey*^ri with two Iznes. 
Tot- other- in/brmatinn see Characteristic sheet. 



Character istie Sheet attached to One Inch Map. O.S. 



MAPS 7 

between first and second class roads has little relation to the 
actual condition of the road. Roads which should be in first 
class condition are pulled to pieces by heavy motor trafific, while 
second class roads are constantly being brought up to first class 
condition. Generally speaking all the roads coloured orange 
are fit for motor traffic, and the uncoloured roads are not. 

Ordnance Survey, ij 126,720, or two miles to one inch. (See 
Plate V.) 

First and second class roads are shown narrower, but still 
coloured orange. The distinction between metalled roads of the 
third class and unmetalled roads disappears. 

" So far as the half-inch maps are concerned the old 
classification of roads is somewhat inadequate to present day 
needs. A committee was formed during 1911-12 to discuss 
the matter.... It is not possible to obtain absolute unanimity of 
opinion on such a subject as the classification of roads on a map, 
but there is no doubt that the classification proposed by the 
committee is a good one, and is an improvement on the former 
classification. It will be applied to the new engraved issue of 
the half-inch maps of Great Britain." {Report of the Progress of 
the Ordnance Survey, 191 2.) 

Ordnance Survey. 1/253,440, or four miles to one inch. 

First class roads only are coloured orange. Second class 
roads are shown by double line uncoloured, and other roads by 
single line. On this smaller scale minor roads are sometimes 
omitted, and this often leads to mistakes, since what ends in 
a farm track often begins as a well made road. In using the 
smaller scale maps it is most important to bear in mind a time 
scale, as explained under that heading. 

France. 1/50,000. 

The principal differences from the system of representation 
employed on the Ordnance Survey are : 

None of the roads are coloured. 

Variety in the signs is obtained by making the two lines 
bordering the road of different intensities. 



I 



8 MAPS 

Where a road passes through a town (shown in red) the 
black hnes cease, and the absence of colour belonging to the 
road is then an especial disadvantage. 

International Map. 1/1,000,000. (See Plates VIII and IX.) 

On this small scale the representation is naturally less 
elaborate. Roads of all classes are shown in red : 

First class by double red line. 

Second class by one continuous and one dotted line. 

Third class by single red line. 

Footpaths, or tracks not suitable for wheeled traffic, by single 
dotted red line. 

None of the roads have any body colour, such as the orange 
of the Ordnance Survey ; and they are all shown very lightly. 
They are scarcely conspicuous enough under the best of circum- 
stances, and when they fall on the redder tints of the layer 
colouring they become almost invisible. (See Plate IX.) 

In general it may be said that all existing topographical 
maps fail in the representation of hill paths. These have an 
importance quite different from paths of equal quality on the 
level. They are very generally well marked and permanent 
features of the ground, and should be shown much more con- 
spicuously than they are. On most maps they are very hard to 
follow when they run through hill-shaded and wooded ground. 
It seems reasonable to demand that all well made and easily 
followed paths in mountainous parts of Great Britain should be 
shown by a single line of orange and black. 

The want of some such convention is particularly marked in 
holiday country. For example, in the Lake District there are 
many paths well made, and as permanent in location, and very 
nearly as obvious to follow, as the high roads. Such are the 
principal ways up Helvellyn, or the path over Grisedale Pass 
from Patterdale to Grasmere. On the half inch map with layers 
these are not shown. Again, in Switzerland the principal paths 
are well made and most elaborately marked with signs and 
patches of colour on the rocks. But it is almost impossible to 
follow these paths on the 1/50,000 map. It would seem that 



MAPS 9 

from the military point of view also it must be of importance to 
show these paths. 

On the other hand, there is a tendency in the modern 
coloured maps to over accentuate the main roads. This arises, 
no doubt, from the fact that as they were originally engraved, in 
black, it was necessary to mark the importance of the main 
roads by showing them in heavy double black lines. Now that 
they have in addition a filling of colour they are often unduly 
prominent, and much diminish the legibility of the contours. 

There is also a tendency to confuse the representation of 
towns by multiplying the yellow coloured roads. A residential 
road in a good neighbourhood is always a first class road in the 
sense that it is broad and well made ; but it is not a main road, 
and probably it should not be coloured yellow. It would be, 
for example, far more easy to discover the main roads out of 
London if all the well made suburban roads were not coloured. 

In a modern coloured map, especially on those of smaller 
scale, it would probably be enough to represent the main roads 
by a single broad line of dark grey, and the lesser roads by a 
narrower line. 

Railways. 

These are almost universally shown in black. There is 
generally a distinction between double or multiple and single 
tracks, narrow gauge railways, and tramways. No provision 
has been made as yet to distinguish between railways worked by 
steam and by electricity; but it is clear that the distinction is 
important, especially from the point of view of public safety on 
the one hand, and of military adaptability on the other. 

Ordnance Survey. 1/63,360. (See Plate I.) 

Railways are elaborately engraved, with distinction between 
double and single lines as in the figure. Embankments and 
cuttings, very important as obstacles or cover, are clearly shown. 

Ordnance Survey. Smaller scales. 

Railways are shown as heavy single black lines, and there is 
no representation of embankments or cuttings. 



lo MAPS 

France, i / 5 0,000. 

Four and two way tracks are in heavy black ; single tracks 
somewhat like the British double track ; narrow gauge lines like 
the British single track ; and tramways distinct from narrow 
gauge lines. There is no general way of showing embankments 
and cuttings. 

Internatio7ial Map. 1/1,000,000, (See Plate VIII.) 

A simpler system, as shown in the plate. A feature not 
generally found is that lines under construction, and also 
projected lines, are to be distinguished. The latter seems to be 
open to objection, since it must be difficult to decide at what 
stage a projected line establishes its right to be shown. 

It is often useful to have special railway maps, in which 
the other topographical features are subordinated. The Swiss 
railway maps are excellent examples of the best system for this 
purpose. The general map is printed in light brown, and the 
railways, with names of the stations, are overprinted in heavy 
black. This is far better than suppressing the topographical 
detail, as is too often done in railway maps. 

The representation of railways running underground through 
towns involves difficulties which have not been successfully 
overcome. 

In a country such as India, where there are several different 
gauges in use, it is most important to distinguish between them. 
And it is even more important in mountainous countries, as 
Switzerland, to distinguish between railways of the ordinary 
kind, rack railways, and funiculars. 

Scale. 

The question of scale is of prime importance ; the aim of the 
map-maker is to show as much as the scale on which he works 
will permit, and he must learn in the first place what are the 
possibilities of the different scales, and secondly how to make 
the most of them. 

The scale of the map is defined by a statement of the relation 
between a distance measured on the map and the corresponding 



PLATE II 
REPRESENTATION OF HILL FEATURES 
One Inch Ordnance Survey Map 





Haahures and Cliff Drawing 



Confusion cf Contours with 
other Detail 





■m^J 

/■/ , ^r^^aA^J:--- ■■■•..1895 ;.,..■•■■" 

J / \ ^ Hccnudir Camv,.- 



Correct Method of Figuring 
Contours 



Misleading' Effect of Unequal 
Vertical Interval in Contours 



Oiiiiminc ,'<iir\-cy. Soutliiniijiii ■/< . /.V/J 



MAPS II 

distance on the ground. The distance on the map will be 
measured in one of the smaller units of length, that on the 
ground by one of the larger ; thus, we say that the map is on 
the scale of one inch to the mile, or one centimetre to the kilo- 
metre, or again, we may invert the statement and say, that the 
scale is one mile to the inch, or one kilometre to the centimetre. 

There is no very definite rule in English practice, whether to 
say, one inch to the mile, or one mile to the inch. In general 
one avoids the use of fractions in the statement : thus, one says 
one inch to the mile, but four miles to the inch, not one quarter 
of an inch to the mile. On the other hand it is common to 
speak of the equivalent in inches of one mile as the characteristic 
of the scale, and to speak of the inch map, the half or quarter 
inch map, and so on. 

This is the common way of speaking, but it is being super- 
seded by the more accurate method of giving the " representative 
fraction," that is to say, the ratio of the distance on the map to 
the distance on the ground. There are 63,360 inches in a mile. 
Therefore the representative fraction of the one inch to the mile 
map is 1/63,360; and the representative fraction of a map on the 
scale of one centimetre to the kilometre is 1/100,000. 

We shall note at once that the British system of measures of 
length produces awkward fractions : for the half inch map the 
R.F. (usual abbreviation for representative fraction) is 1/126,720; 
and for the quarter inch map it is 1/253,440. This arises of 
course from the fact that the number of inches in the mile is not 
a round number. In countries where the metric system is used 
this difficulty does not arise, since all the units of length, large 
and small, are related decimally. It follows that the R.F. for 
a map of such a country is naturally a round number, and it has 
become the practice to speak of " natural scales," meaning 
thereby, scales for which the R.F. is a round number, 1/250,000, 
1/100,000, 1/80,000, and so on. The term does not seem to be 
a good one, since there is not anything natural in the use of a 
decimal system of units, but rather the contrary, if it is proper 
to argue from the fact that the metric system, a late creation, 
has not yet displaced altogether the complicated non-decimal 



12 MAPS 

systems which natural man had evolved. Natural scales, in fact, 
are natural only in countries which have become habituated to 
the decimal system of measures ; in other countries they are not 
natural, but their scientific convenience has led to their gradual 
introduction. 

We may notice that there is some diversity of opinion as to 
the choice of a convenient range of so-called natural scales : 
Shall the series run 

1/200,000, 1/100,000, 1/50,000, 
or shall it run 

1/250,000, 1/125,000, 1/62,500 ? 

There is an undoubted convenience in subdivision by two, so 
that a sheet on one scale is subdivided into four sheets on the 
scale next larger, and so on. This appears in either series. 
But the second series is derived by such steps from the one in 
a million scale, while the first is not. On the other hand the 
numbers in the first series are simpler, more round, than the 
numbers in the second. The divergence illustrates very weir the 
difficulty that continually occurs in the application of any purely 
decimal system, that for many purposes continual division by 
two is more convenient than division into so many tenths. 

Again, there is the advantage in the second series of scales 
that it differs very little from the series in inches to the mile. 

Half an inch to the mile is 1/126,720. This differs from 
1/125,000 by little more than one per cent., or about the un- 
certainty in the scale of the printed map which is due to the 
expansion of the paper with damp. Hence in all ordinary use 
of the map there is no practical difference between the two, and 
this fact certainly tends to the choice of the series derived from 
the one in a million by continual division into halves. More- 
over, the recent standardisation of the one in a million map, and 
the convenience of making all other sheets subdivisions of this, 
must tend to the adoption of the second series rather than the 
first. 

It seems probable, therefore, that the series 
1/250,000, 1/125,000, 1/62,500 
will gradually be adopted more and more widely. 



MAPS 13 

Method of writing the Representative Fraction. 

It is not unimportant to remark that the R.F. is better 
printed 1/126,720 or i : 126,720, than in the fractional form y2^r2o> 
which requires figures so small that they are read with difficulty. 

There can be no hard and fast rule as to the scales suitable 
for maps intended for definite purposes. But in general one 
may say that cadastral maps are larger than 1/15,000; topo- 
graphical maps between 1/20,000 and 1/1,000,000, the larger 
scales being for military purposes tactical maps and the smaller 
strategical ; while anything on a smaller scale than one in a 
million can hardly be considered topographical, but may be 
called for convenience an Atlas map. 

Construction of scales for maps. 

The word scale is used in two senses. In an official manual 
we find on consecutive pages these two statements : 

" The scale of a map is the relation between a measured 
distance on the map and the corresponding distance on the 
ground." 

" The scale of a map should be, for convenience, about six 
inches long." 

In the second sense the scale of a map is the diagram which 
allows one to translate distances on the map into distances on 
the ground expressed in any unit desired — not necessarily that^ 
employed in the first instance when the map was made. Thus 
it may be convenient to put on an inch to the mile map a scale 
of hundreds of yards ; or to construct a scale of miles for a 
French map on 1/80,000. 

A scale should be constructed so that any length taken from 
the map with a pair of dividers can be read off at once from the 
scale. 

Suppose that the scale is to give thousands and hundreds of 
yards. 

The main scale is divided simply into thousands of yards, 
set off to the right of the zero. To the left of the zero one 
additional space of a thousand yards is subdivided into hundreds, 
and if it is numbered at all, which is usually not really necessary. 



14 MAPS 

it is numbered to the left, that is to say, in the opposite direction 
to the numbering of the main scale. 

A few moments' trial will show the advantages of this plan. 
Suppose that the distance is between 3000 and 4000 yards. 
One leg of the dividers is set on the division 3000 ; the other 
leg reaches beyond the zero, and the odd hundreds are read off 
from the subsidiary scale. On this system the actual figures 
required are read directly from the scale. On any other system 
the figures shown by the scale must be modified in some way or 
other. 

Example : For the one inch to the mile map, construct a scale of 
thousands and hundreds of yards. 

1000 yards = 1000/ 1 760 inches = o"568 inches. 

p-mrrmr] 1 1 1 \ 1 

1 2 3 4 5 

Fig. 2. Scale of thousands of yards, for the one inch to the mile map. 

Note that : 
(i) If the zero were placed at the extreme left of the scale, 
or (2) If the subdivided portion were numbered from left to right, 
or (3) If the scale had been constructed for the unit 500 yards instead of 
1000 yards, 
it would not have been so convenient as in the above form. 

The scales given on the Field Service Protractor will generally serve for 
the construction of any desired scale without calculation. 

Problems in the construction of scales. 

Exercises in the construction of scales are often set in 
military examinations, and many rules for the solution of these 
problems are given in the military textbooks. It seems to the 
author that these rules, like the old fashioned multiplicity of 
rules in arithmetic, defeat their purpose by suggesting that there 
is a rule to be remembered, instead of a common sense sum to 
be worked. 

Thus, for example : Given a map on the scale 1/100,000 : To construct 
a scale of miles. 

On the scale one mile to the inch the R.F. is 1/63,360. For the smaller 
scale 1/100,000 one mile is obviously 63,360/100,000 or 0*63 inches, and the 
scale is easily constructed with a rule graduated to inches and tenths, or 
with the diagonal scale of the protractor. 



MAPS 15 

Rivers. 

Rivers and streams should be always shown in blue. Their 
importance is great, not only the obvious importance which they 
possess as sources of water supply, means of communication, or 
obstacle to getting across the country, but the subsidiary yet 
very real importance which they derive from their use in helping 
realisation of the relief of the land. When the streams are shown 
conspicuously in blue they make it easy to follow the run of the 
valley bottoms, and to distinguish valleys from ridges. (See 
Plates IV and V.) 

The characteristic sheets attached to the maps of the 
Ordnance Survey (see Plate I), give no information as to the 
methods of representing rivers and streams. In general a stream 
more than fifteen feet broad is represented by a double blue 
line on the one inch map, and perhaps also on the maps of 
smaller scale. There are no special signs for locks, wiers, or 
falls ; and there is no indication of the navigibility or otherwise 
of the stream. Nor is there any distinction between natural 
streams, canalised streams, and wholly artificial canals. Con- 
fusion is avoided, however, by the consideration that the shape 
of natural and artificial waterways is very different, and that the 
latter tend always to run along the contours. 

But the need for some distinguishing sign is sometimes very 
conspicuous, as in the map of Dartmoor. Here there are many 
"leats" or small canals for water supply of towns or of 
mines. These naturally run along the contours, or nearly so. 
Occasionally they cross the course of a natural stream by an 
aqueduct. But there is not on the Ordnance Survey maps any 
sign for or representation of this aqueduct; and consequently 
the maps show the impossible feature of a stream dividing into 
three. At first sight it appears that a contour has been shown 
blue instead of red, in error. The absence of any sign of the 
aqueduct by which the leat crosses the stream is a serious 
blemish on the map. 

A further difficulty is sometimes caused by the failure to 
show streams that run in deep ditches by the roadside, which 
is not uncommon in flat country such as the fen districts of 



1 6 MAPS 

England. It should be easily possible to show the necessary 
blue line alongside the black line which borders the road ; its 
absence makes it impossible to discover what becomes of a 
stream which runs by the roadside. 

In general a stream will cut a contour at right angles to its 
general direction, the contour being thrown back upstream 
where it crosses. When the fall of the stream is rapid, and 
particularly when the ground is rocky, the contours are V-shaped 
at the crossing ; when the ground is flat and alluvial the crossings 
of the contours are more rounded. It is clear that in general 
a stream cannot cross a contour more than once. There are, 
however, exceptions to this rule which are at first sight puzzling. 
They occur in very flat country, where the streams are some- 
times confined by banks much above the level of the ground on 
each side. In such cases it is possible for a stream to cross 
a contour several times. It would be well that streams of this 
character should be distinguished by some special sign, for they 
are important from the fact that it is easy to breach their banks 
and flood the surrounding country. 

The characteristic sheet of the French 1/50,000 map distin- 
guishes between important rivers, shown double ; streams, shown 
by single lines ; and canalised rivers, margined by thick blue 
lines, with signs for locks. Bridges of stone, steel, and wood ; 
suspension and swing bridges ; ferries, and wiers, are all given 
conventional signs. 

The International Map has a quite different set of signs, 
suitable to its smaller scale. Perennial rivers are shown by 
a solid blue line of varying width ; non-perennial are heavily 
long-dotted. Unsurveyed rivers are lightly dotted ; and navi- 
gable rivers are shown by a double line. Navigable canals have 
cross strokes similar to those often used for railways, and non- 
navigable are distinguished from natural streams by their 
uniformity. There are signs for rapids and falls, and for the 
limit of navigation. 



PLATE III 



CONVENTIONAL SIGNS 




y f 




^ , Flat s 







-;:;-'''— 




<0'^ 




'^^'Kii 


' ' ' "" / 


' 


'/ 


M ,/■/ 


,.r..^e 


1' r'y.^J^ji. 


'" I 




/ 


;'\ y. H„. > 




Itl .-/..»,.., 


- 


i 


^ 


'" 1 t1 




,S' < U /I </ 




^r-^^^ix ^ i'-^jf^^^ ^^ 


ISLj 



National Boundary 



Rock and Water Linen 



Orthitirirc .SV 



•nil, „„n<h„l. 1913 



MAPS 17 

Woods and forests. 

In black engraved maps these are shown by small tree signs, 
sometimes, as in the Ordnance Survey one inch map, of two 
varieties to distinguish between deciduous trees and conifers 
which are mostly evergreen. (See Plate II.) The effect is 
heavy, obscuring details, and rendering names almost illegible. 
On the British coloured maps the woods are overprinted with a 
tint of bright pale green. (See Plate IV.) This brings them 
out, perhaps somewhat too conspicuously, but leaves the under- 
lying detail of roads and names more illegible than ever. The 
smaller scale half inch and quarter inch maps have the same 
system. 

It seems to be decidedly better to leave out the tree signs, 
and to show woods by a uniform tint of green, except on layer- 
tinted maps, where the woods shown thus become confused with 
the tints representing height. In the latter case the woods may 
be shown by tree signs printed in green, as in the International 
Map, though this is hardly clear enough on the green layers. 

The French 1/50,000 map shows woods in green tint, without 
tree signs ; and has special signs for nurseries, gardens, and 
vineyards. Where tree signs are used trees in rows denote 
orchards, while trees irregularly disposed denote woods. The 
International Map, on the small scale of 1/1,000,000, has no sign 
for orchards and vineyards, which are seldom so extensive that 
they need be shown on this scale. It remains to be seen how 
they will be shown on those sheets of France, Germany, and 
California where the vineyards and orchards are of great extent, 
and might be shown. 

Sheet margins. 

It is important that all margins of sheets should be divided 
in latitude and longitude, and that the origin of the system of 
longitudes should be stated clearly. 

It is also desirable that the margins should be divided into 
sections of some convenient unit of length, and that each section 
should bear a letter or a number, to provide a ready means of 
referring to a particular region of the map, 

H. M. s, 2 



I 8 MAPS 

It is further desirable that the margins of contiguous sheets 
should overlap to some extent, so that it should never be 
necessary to refer to two sheets for the detail of a small district. 
The inconvenience of having a town or village on the extreme 
edge of the sheet is sufficiently obvious ; yet no general attempt 
has been made to provide overlaps in the sheets of any topo- 
graphical series. Some of the sheets of the large sheet series of 
the half inch map of England overlap north and south, but not 
east and west ; and on the one inch map there are sheets which 
overlap irregularly rather than show a large extent of empty sea. 

On the French 1/50,000 map there is a partial attempt to 
mitigate the inconvenience of having important detail cut in two 
by the sheet margin. East and west, and to a very slight extent 
north and south, there is room to show important detail beyond 
the strict limits of the sheet ; but the principle upon which the 
irregular boundary is drawn is not clear ; and there does not 
seem to be any advantage over the plan of making all the sheets 
overlap by a definite amount. 

It is highly convenient to have the sheet divided up by lines 
drawn right across it ; and in general it would seem that these 
lines should be the meridians and the parallels of latitude. The 
map is thus divided into trapeziums, and there is no reason why 
they should not be distinguished by letters and numbers to 
facilitate reference, as is very commonly done in atlases. There 
is, however, a certain advantage in dividing the map into squares 
rather than into trapeziums; it much facilitates the enlargement 
of small pieces of the map by the method of squares. For this 
reason all the recent half inch maps of Great Britain are divided 
into squares of two inches to the side, while the meridians 
and parallels are not carried across the sheet. This system 
is especially appropriate to the British sheets, which are 
rectangular, and not bounded by meridians and parallels, as 
more modern sheets are. There seems to be no reason why 
both systems should not be used, provided that the two sets of 
lines were printed in different colours. (See Plate V.) 

In the use of the British squared maps it is most important 
to avoid the very common mistake of supposing that the vertical 



MAPS 19 

sides of the squares are meridians ; they may be as much as four 
degrees out of the meridian. Yet it is common to find such 
statements as that for '' practical purposes " the edges of an 
Ordnance Survey sheet may be considered north and south. 

The sheets of the Ordnance Survey, unhke most, have on 
their margins a diagram showing the true meridian and the 
magnetic meridian of a given date, with a statement of the 
amount of the variation of the magnetic meridian annually. It 
is, however, not safe to use this diagram for the purpose of 
laying off either true or magnetic meridians. The lines shown 
are too short, and they are too close to the edge of the sheet for 
■convenient use. Moreover on some at least of the sheets they 
are not accurate, having become a kind of conventional sign, in 
which the angle as engraved does not correspond with its 
numerical value as stated, while there is no means of knowing 
which if either of the meridian lines is engraved at its proper 
inclination to the margin of the sheet. This is particularly 
■embarrassing in the use of the large sheet series of the one inch 
map, from which the division of the meridians and parallels has 
most unfortunately been omitted. 

The representation of hill features. 

The real difficulty in mapmaking is to represent the relief of 
the ground. This is naturally so, for we are trying to find 
a method of representing a solid figure by drawing on a flat 
sheet, or to represent three dimensions in two. Moreover, we 
have not a free hand to do the best we can with this particular 
problem, but are limited by the condition that we must not 
obscure the other details on the map. 

Until the last few years little progress was made in the 
solution of this problem. So long as the map was printed in a 
single colour, almost necessarily black, very little could be done. 
Recent improvements in the processes of colour printing have 
made it possible to produce maps in colour, sometimes with 
twelve or fifteen separate printings. This has altered completely 
the conditions of the problem, and, while great progress has been 
made already, it seems probable that much more may be done. We 
shall therefore discuss this part of our subject as fully as possible. 



20 MAPS 

The relief of the ground may be shown in a number of 
different ways : by hachures or hill-shading ; by contours ; by 
spot heights ; by hypsometric tints, generally called in England 
" the layer system." And these methods may be, and usually 
are, combined so that three or four are in use on the same map. 
We shall begin by considering them separately, and then discuss 
how they may be used in combination. 

Hachures. 

Hachures are lines drawn down the directions of steepest 
slope. On slight inclines they may be delicate and not too 
close together. As the slope gets steeper they may be drawn 
heavier, and be closer together. If they are drawn faithfully 
they are very expressive, and give a good idea of the shape of 
the ground. But the system of hachuring has the following 
defects : 

Its range is small ; that is to say, it is impossible to show 
many different degrees of slope. Slight folds in the ground, if 
they are shown at all, are exaggerated ; really steep slopes 
cannot be shown proportionately heavy without obscuring all 
other detail. Moreover, it is impossible to preserve uniformity 
of treatment on the different sheets of one and the same map. 
The steepest slope on a sheet of nearly flat country may be 
actually less steep than a relatively moderate slope on a 
mountainous sheet ; and slopes which are important in the 
former may be insignificant in the latter. Hence hachures can 
be used to indicate that there is a slope, but they cannot give 
much information as to the absolute degree of the slope. 

It is difficult to draw hachures properly in the field ; and 
when the field sheets come into the hands of the engraver it is 
certain that they will be improved in appearance, and generalised,, 
so that they beconie untrustworthy in detail. 

Hachures, then, belong to the days of delicate and expensive 
engraving upon copper, and with the changing conditions of 
map reproduction they are rapidly becoming obsolete. Excellent 
examples of the system are to be seen in the old engraved sheets 
of the one inch Ordnance Survey maps of the United Kingdom 
(see Plate II), and in the older maps of Switzerland ; and it 



MAPS 21 

survives on the modern colour printed maps that have as their 
basis transfers from the engraved plates. (See Plate IV.) But 
it is not probable that hachures would be used nowadays on any 
entirely new series of maps. 

The term hachure has the definite meaning assigned to it 
here, and should not be confused with hill-shading, described in 
the following paragraph. It is regrettable that in the 19 12 
edition of the Manual of Map Reading the distinction between 
hachures and hill-shading is not maintained. 

Hill-shading. 

Hill-shading aims at producing very much the same effect as 
hachures in an easier and cheaper way. The draughtsman 
colours the slopes in rough proportion to their intensity, with 
brush or stump. The drawing is then photographed and a hill- 
shading plate produced in "half-tone," by a process similar to 
that by which photographic illustrations are produced in books 
and newspapers. Thus hill-shading consists of series of dots, 
whereas hachuring consists of series of lines ; and the two are 
very easily distinguished. (Compare Plates IV and V.) 

It is difficult to do hill-shading effectively in the field, and it 
is generally added by the draughtsman in the office ; but since 
it is in its nature more generalised than hachuring, and is quite 
unsuitable for showing detail, this is of small consequence. 

Both hill-shading and hachuring suffer from the defect that 
they do not readily show which direction is uphill and which is 
downhill. By themselves, in fact, they cannot give any indication 
at all on this important point. A ridge and a valley, each with 
shaded sides, cannot be distinguished one from the other simply 
by the shading, and one must rely on other details, such as 
rivers in the valley bottoms, or heights marked at various places, 
to indicate the interpretation of the shading. A sheet with hill- 
shading and nothing else might be interpreted equally well in 
opposite ways. 

We are speaking now of shade which depends only on the 
degree of slope, without any convention as to the way in which 
the shade is cast ; without, indeed, any possibility of imagining 



22 MAPS 

it as a shade produced by contrast with Hght from a definite 
source. It is sometimes spoken of as vertical shade — an ex- 
pression which can have none but a conventional meaning ; in 
other places it is called the shade cast by a vertical light, which 
is meaningless. These expressions serve, however, to distinguish 
it from the other form of hill-shading, which represents the 
shadow which would be cast on the ground by oblique light 
from a low source, such as the sun near setting. For some 
reason which is not clear the source of light is generally 
imagined in the north-west. Oblique hill-shading is very much 
used in European maps, and it produces a strong effect of relief. 
But it has the disadvantage that it makes the slope in the 
shadow look steeper than the slope in the light, left unshaded. 
In fact it is only by induction that one gets any suggestion at 
all of the slopes towards the light. 

We may compare thus the effects of the vertical and the 
oblique s}\stems of shading. Imagine a ridge and a valley, each 
running north-east, with the slopes on each side the same. Under 
the vertical shade they would be indistinguishable. Under the 
oblique shade they would be readily distinguished one from the 
other ; but the ridge would appear steeper on its south-east side, 
the valley on its north-west side. 

To avoid this difficulty an ingenious system has been devised 
for the new map of France on the scale of 1/50,000. The map 
is hill-shaded on both systems, printed in different colours. 
There is a vertical shade in bistre, and overprinted is an oblique 
shade in purple grey. On moderately undulating ground the 
effect is excellent ; in mountainous country the colour becomes 
too heavy. And the system is of course expensive. 

It is clear that no s\-stem of hill-shading can give any 
information as to the actual height of the ground above sea 
level. Hill-shading should therefore be considered as a means 
of bringing up the relief of the country graphically, to supple- 
ment the more precise information which can be given in other 
ways. This being so, it is important to notice that the hill- 
shading should be kept very light. The least tint that will serve 



MAPS 23 

to show the difference between one side of a hill and the other 
is enough, since the degree of slope should always be denoted 
by the closeness of the contours. Hill-shading often suffers 
from being too heavy, as in the half inch O.S. map. (See 
Plate V.) A pale transparent grey, as in the 1/250,000 Bavarian 
Staff map, is probably the best colour. 

Spot heights. 

Spot heights are the heights above sea level marked at 
various points on the map. They are sometimes called spot 
levels ; but the misuse of the word level in this connection is to 
be condemned. 

On cadastral maps the height of each bench mark is usually 
given ; these are not strictly speaking spot heights, since they 
refer to the height of the bench mark, not of the ground. The 
heights which, on the British cadastral maps, are given along 
the crown of the road are spot heights, and a selection of them 
is given on the smaller scale topographical maps. There is 
a strong tendency to give spot heights for summits, and not for 
the bottoms of depressions. 

Spot heights are very useful as exact points of reference, but 
they cannot by themselves give any idea of the form of the 
country. 

Contours and form lines. 

A contour is a line joining a series of points which are all at 
the same height above mean sea level. If the sea suddenly rose 
a hundred feet the new coast line would follow the hundred foot 
contour. 

A form line is an approximate contour, not accurately 
surveyed, but sketched upon the ground. 

There is some difference of practice in the use of the two 
expressions, but for our present purpose it is not material to 
define the precise difference in degree of accuracy which divides 
contours from form lines. It will be sufficient to keep the term 
contour for the product of instrumental methods, even if rough, 
and to call the much less accurate contours which are merely 
sketched, form lines. 



24 MAPS 

Thus, the Ordnance Survey maps (Plates IV and V) have 
contours ; the Basutoland map (Plate VI) has form lines. 

Contours give a maximum of precise information with a 
minimum of obstruction to the map. They may be considered 
the standard method of showing relief, to which all others are 
subsidiary. But to be effective they must be drawn on carefully 
■considered principles. 

Contours should be drawn at uniform intervals of height ; 
any departure from this rule is certain to lead to inconvenience.. 
(See Plate II.) The interval chosen will naturall}' be a simple 
multiple of the unit of length employed : 50 or 100 feet ; 10 or 
20 metres. 

The contours must be numbered ; and when possible they 
should be numbered according to the rule adopted in the British 
one inch map : 

The figures stand on the contours on the 7ipper side. (See 
Plates II and IV.) 

It is somewhat strange that this excellent rule is not followed 
in the later maps of the Ordnance Survey, for it affords a ready 
means of distinguishing between uphill and downhill. To do so 
it is not necessary that the map should be examined so closely 
that the figures of the height may be read. So long as one can 
see the places in which the figures are, one can see at once which 
way is uphill, for the figures stand on the contours on their 
upper sides. 

The annexed figure shows the one way which is right and 
the three ways which are wrong, according to this principle of 
figuring the contours. A comparison of the British one inch 
map with any other map will show the undoubted advantage of 
this method. It fails only when the contours come so close 
together that there is not space to draw the figures between 
them. In such cases, and in no other, the number must be 
inserted in the line of the contour. A close scrutiny is then 
needed to discover in which direction the numbers increase, and 
the map is much more difficult to read. 

When the country is steep the contours come close together, 
and it is difficult for the eye to follow them, even on close 



ORDNANCE SURVEY OF ENGLAND 



PLATE IV 



One Inch Scale 63,360 




In Outline, without Hills 




In Colour 



On/iuiHi-c Si,r>,-v. .y<>ii//i>ini/'/''ii , /:i/.'j 



MAPS 



25 



examination ; while if one tries to obtain a general view of the 
map, the contours merge into one another, and become a mere 
shade. Many of the Swiss maps suffer from this defect. 

In such cases it is necessary to guide the eye by accentuating 
every tenth or every fifth contour. If, for example, the map is 
contoured at ten metres interval, every tenth contour, that is to 
say, the hundred metre contours, should be drawn heavily. This 




(«) 





Fig. 3. Methods of figuring contours. 
(«) right; {b), {c) and {d) wrong. 



enables the eye to follow the run of the contours, and is a great 
help in reading the form of the ground. It tends to give the 
map a stepped appearance, and isolated hills seem to be ridged 
like oyster shells, as may be seen especially in the 1/62,500 
maps of the United States. But this is a small matter in com- 
parison with the real advantage of being able to follow the 
contours readily. 



26 MAPS 

The worst way of accentuating each tenth contour is to 
chain-dot it, as in the Swiss maps on the scale of 1/50,000. 
These dotted contours, which are the only ones figured, dis- 
appear except under close attention, and the whole system 
becomes nearly unreadable. It is instructive to take one of 
these maps and to ink in the dotted contours, thus rendering 
them heavier than the rest. Immediately the map becomes 
readable. 

We have said that the contour interval must be equal 
throughout, and that any departure from this rule is very 
inconvenient. There are certain cases in which it may be 
legitimate, indeed necessary, to interpolate intermediate con- 
tours. For example, in flat country nearly at sea level, such as 
the fen country in the East of England, there may be a large 
area which is all comprised within a single contour interval, and 
in such cases an elevation of a few feet may be more important 
than a rise of several hundred feet in more elevated regions. 
Intermediate contours at close intervals are then very useful ; 
but it is evident that they should be readily distinguishable from 
the contours of the normal series. They may be chain-dotted, 
or distinguished in some other way. But they should not be 
drawn exactly like the others, as is done in the British one inch 
maps, which show the 50 foot contour, and above that only the 
100 foot contours up to 1000 feet. 

A more serious defect of the British map is that above 
1000 feet the contour interval becomes 250 feet, and higher up 
the interval becomes wider still. This is destructive of all 
facility in reading the map, as may be seen at once in the 
example appended. (Plate II.) At 1000 feet all the slopes 
suddenly seem to become less steep, and it is very hard to train 
oneself to ignore this misleading appearance. If the objection 
is made that in every steep country contours at uniform intervals 
come so close together that they can leave no room for any 
other detail, one may reply that in country so steep as this there 
is little detail to show, except the contours ; and that the close- 
ness of the contours gives the effect of hachuring or hill-shading, 
with far greater precision than the latter is capable of. 



MAPS 27 

It is desirable to have some guide to the choice of the 
contour interval. An examination of the best examples of 
British and foreign maps shows that the rule 

Contour interval = 50 feet divided by the mtmber of incites 
to the mile 

represents pretty well the result of experience. It should be 
understood, of course, that this rule is entirely empirical, derived 
simply from a number of maps treated as experiments. 

Layer colouring, or hypsometric tints. 

The layer system, as it is generally called in English, is a 
comparatively new system which improvements in colour print- 
ing have rendered possible. Its aim is to give to the map 
the general effect of relief which the contours alone cannot give, 
because they can be read over only a small piece of the map at 
one time. A scale of gently graded colour tints is chosen, and 
all the ground which lies between two certain contours is 
coloured a certain tint, while that included between the next 
pair of contours is coloured to the next tint on the scale. 

An early example of the use of the layer system is found in 
the well-known half inch maps of the United Kingdom produced 
by Mr Bartholomew. More recent examples are the Ordnance 
Survey half inch map (Plate V) ; several Continental maps, 
notably the Bavarian General Staff map ; and lastly, the new 
International one in a million map of the World. (Plates VIII 
and IX.) 

The layer system is exceedingly effective in country which 
is suited to its use ; and it is very often exceedingly unsuccessful 
in general use. We will examine it in some detail. 

It is successful in country which does not require more than 
seven or eight contour intervals. The colour scale can then be 
formed of eight tints of one colour, and progress from light to 
dark or from dark to light will denote progressive increase in 
height, while even the heaviest tint will not seriously obscure 
the underlying detail of the map. Where more than eight 
tints are necessary it is difficult to ensure that the heavier tints 
shall be transparent enough to leave the detail legible ; and it 



28 MAPS 

becomes necessary to pass from one colour to another. At this 
point difficulties begin. 

It is not possible to work up in tints of one colour to the 
point of change, from light to dark, and begin the new colour 
with the lightest tint, for the contrast is then too violent ; the 
scale must be inverted at the change of colour, and if the first 
series ran from light to dark, the next must run from dark to 
light. This inversion of the colour scale introduces difficulties 
in reading the map, which it seems to be impossible to avoid. 
They can, however, be diminished by care in choosing the colours 
of which the scale is composed. It is asserted, and apparently 
rightly, that the change from one colour to another is least 
disagreeable when the colours run in their spectrum order, A 
colour scale which runs from green through yellow to orange 
and red is more agreeable than one which passes from green to 
orange without the intervening yellow. How far this principle 
rests on physiological foundations is not at all clear ; but it 
seems to be true in effect. Undoubtedly the most successful 
layer system maps are those which follow this rule in the 
selection of the colours for the scale of tints. 

A more serious difficulty is that even when this system of 
choosing colours is pushed as far as possible, it is still impossible 
to provide enough tints to serve for a great range of layers at a 
uniform contour interval. And were it possible to select the 
tints, the number of printings required would be prohibitive. It 
is necessary, therefore, in the higher ground, to widen the interval 
which is represented by one tint (Plate VII, Afghanistan); and 
this produces the same inconveniences as the wider spacing of 
the contour interval produces in contoured maps without the 
layers. This difficulty is felt especially when the country to be 
represented is a high plateau, such, for example, as the Trans- 
vaal. In such a case differences of a hundred feet are as 
important as they are at sea level ; yet if a uniform scheme 
were applied throughout they would be shown by differences of 
colour in the latter case and not in the former. It is not easy 
to see how to overcome this difficulty. 

A good deal may be done, however, by drawing in the 
contours at uniform vertical intervals (as in the Kenhardt sheet, 



ORDNANCE SURVEY OF IRELAND 



PLATE V 



1 



Half-inch Scale 126,720 



Malm Say 




With Hill Shading 



Malm Bay 




Layer System 



Onhian/x Survey. Soutluiiiiploii . 1913 



MAPS 29 

Plate IX), even if it is not possible to assign a separate tint to 
each interval. The advantage of this may be seen on comparing 
the Bavarian Staff map with, let us say, the layer map of 
Scotland. In the former several contours are included in the 
limits of a single tint, on the higher ground ; in the latter this is 
not done. There can be no doubt that the former is the more 
effective. 

Combined systems of showing relief. 

We have discussed separately the merits of spot heights, 
hachures and hill-shading, contours, and colour layers. In 
practice several of these systems are generally used on one 
map. 

Contours and hill-shading make an effective combination, 
and if the contours are drawn strongly they make it possible 
to use oblique shading without much danger of the slope in 
the shade looking steeper than the slope in the light. (See 
Plate V.) 

Hill-shading combined with layers demands great skill in 
its application, or the shade changes the tint of the layers, and 
gives a misleading effect. On the other hand, a layer map with- 
out hill-shading is very liable to look flat in the higher regions, 
where the layer interval is large. (See Plate IX.) 

The merits of any combination cannot be discussed with 
profit, except by reference to particular maps. We will there- 
fore defer criticism until we discuss in some detail the best 
existing examples of topographical maps of all countries. 

Other conventional signs. 

It is hardly possible within the limits of this book to give 
a complete account of the many other conventional signs 
adopted in different series of maps. A study of the conven- 
tional sign sheets of the different survey departments will show 
how varied are the ideas of what is desirable. Some of the 
signs for the Ordnance Survey are shown in Plate III. 

The tendency of modern map-makers is to elaborate the 
conventional signs. The new French map on the scale 1/50,000 
is an example, and the special maps for the use of aviators go 



30 MAPS 

much further. We shall discuss the difficult question of aero 
maps in a separate section. 

Until recently it was the rule in British maps that no 
military or naval works were to be shown, and that no contours 
were to be shown within 5000 yards of any fortification. The 
result of this rule was that the public maps of garrison and 
dockyard towns were meaningless, which probably caused as 
much trouble to the Services as to the public, though of course 
there were complete confidential editions. As a precaution 
against knowing the position of a fortification the rule by its 
strictness defeated its own object, since it was easy to mark the 
points where the contours were suddenly discontinued, to draw 
the circle through those points, and to conclude that a fort was 
at the centre. The newly published smaller scale maps now 
show the positions of the forts, and the contours have been 
completed. 

Map reading. 

Facility in reading from a map all the information that is 
implied in its conventional representation of the ground is an 
accomplishment only to be attained by constant practice in the 
field, and it is useless to attempt to lay down many rules for it. 
Much excellent advice on the methods of learning the art is 
given in the Manual of Map Reading and Field Sketching; 
and we will not attempt to cover again the ground which is 
thoroughly gone over in that book. But we will try to supple- 
ment what is said there by a few additional notes. 

Sections and profiles. 

In the solution of many practical problems it is required to 
draw a section across the country, from the information which 
is given on the topographical map. Suppose a line drawn 
across the map along the line of the proposed section : it will 
cut the contours at a number of points, and these points will 
furnish the principal material for the construction of the section. 
Lay a strip of paper along the line, and mark on it the points 
Avhere the line cuts each contour. Draw perpendiculars from 



MAPS 31 

the edge proportional in length to the heights of the contours 
above sea level : this will be facilitated if the paper is furnished 
with equally spaced lines parallel to the edge, and distant from 
one another by the contour interval on the adopted vertical scale 
of the section. 

A broken line joining the summits of these perpendiculars 
is a rough approximation to the section, which can be much 
improved by studying the other indications of height upon the 
map. Thus, it is improbable that a spot height will fall exactly 
on the line of the section, but a good deal may be learned from 
those that fall near. Hill-shading is useful in suggesting the 
probable shape of the country between the contours, and care 
should be taken to utilise the information which is given b}'- 
streams. By taking advantage of these subsidiary sources of 
information it is possible to construct a fairly good section from 
a topographical map ; and of course the closer the contour 
interval the more accurate the result. 

It is however inevitable that a section drawn in this way 
should be conjectural in its details, and if accuracy is required 
it is necessary to run a line of levels across the country along 
the line of the section. For this process we refer to the chapter 
on Levelling (page 95). 

A profile of a road is a section run along the course of the 
road, instead of straight across country. It is constructed in 
the same way as a section, by laying a strip of paper along 
successive lengths of the road and marking off the points where 
the contours are crossed. In addition there are generally a 
number of spot heights marked along the road, and these are 
especially useful because they give summits. When a road 
rises above a contour and falls below it again there will usually 
be found an intervening spot height, which will mark the 
summit. 

It is often useful to have the profile of a road along which 
it is necessary to send traffic, and profiles of the main roads 
of the country are being published for the use of motorists. 
Unfortunately the makers of these books have adopted the 
wrong name " contour road book," instead of " profile road 
book." This bad mistake should be avoided. 



32 MAPS 

Problems of intervisibility. 

Questions on the use of maps very often demand the solution 
of the problem, whether one point is visible from another. It is 
evident that this can be solved, in some degree, by drawing a 
section from one point to the other, and seeing if any intervening 
point on the section rises above the ray joining the given points. 
Since the section can be only approximate it is clear that caution 
must be used when the ray clears the intervening ground by only 
a little. 

In most cases it is not necessary to draw more than a part, 
if any, of the section, for it is easy to see where are the critical 
points. 

It should never be forgotten that in undulating wooded 
country the trees are the principal obstacles to mutual visibility 
of points, and it is not possible to estimate from the map the 
effect of the trees. Hedgerow trees, which are not marked on 
the map as woods, since they offer little obstacle to the passage 
of men, are often a complete obstruction to the sight. Conse- 
quently problems of mutual visibility of points are more useful 
in testing the understanding of the map than in deciding whether 
it is actually possible to see from one point to the other. 

Reconstruction of the view from a given point. 

It is an excellent exercise in map reading to try to recon- 
struct from the map the view of the country from a point of 
vantage, and to draw it as a panorama. From the chosen point 
of view radiating sections are run across the country, and it is 
usually not hard to discover what heights form the sky line in 
different directions, and what features are prominent in the 
middle distance. When these are determined, a study of the 
contours gives a general idea of the shape which these features 
will present, and then by the exercise of some ingenuity it is 
possible to construct a panoramic sketch which reproduces the 
broad features of the view. A few exercises of this kind are 
very useful in teaching facility in reading relief, especially in 
town schools where it is difficult to reach actual ground on 
which to practise. 



MAPS 33 

Identification of distant objects. 

It will often happen that a wide view, say in the Lake 
District, or on Dartmoor, presents a confused panorama of 
peaks which cannot be identified by their relations to one 
another as shown on the map. To identify such a distant 
object it is necessary to take its bearing by compass, subtract 
the westerly deviation, as given on the margin of the Ordnance 
Survey map, and with the protractor to lay off a line on the 
resulting true bearing from the point of observation. For the 
instrumental process reference may be made to page 105. 
The distant object will then lie on this line drawn upon the 
map ; and of the several objects at varying distances which may 
chance to lie on it, it will not in general be difficult to select the 
right one. 

The reverse problem sometimes arises. It is desired to 
identify on the ground, or at least to discover in what direction 
it lies, an object which is marked on the map, but which is not 
apparent to the sight. In such a case draw on the map a line 
from the point of view to the object in question, measure with 
the protractor the true bearing of this line, and add the compass 
deviation west. Then with the compass to the eye turn slowly 
round until some object is found which has the given compass 
bearing. The object sought will lie in the same straight line 
from the observer, and with this indication it is often possible to 
discover it, or at any rate to find exactly where it lies. 

Measurement of areas. 

The first consideration which arises in this problem is : are 
the areas correctly represented on the map ; or is the projection 
on which the map is constructed an equal area projection. 

Topographical maps are not usually constructed on a pro- 
jection which is theoretically an equal area projection ; but the 
misrepresentation of areas will always be much less than the 
uncertainty which is introduced by the expansion and contrac- 
tion of the paper with damp. 

Atlas maps will very often be on projections which mis- 
represent areas grossly ; but for a consideration of this question 
H. M. s. 3 



34 MAPS 

reference must be made to a treatise on the somewhat intricate 
subject of Map Projections. 

An easy way of measuring areas on a map is by superposing 
a sheet of tracing paper regularly ruled in small squares. First 
count the number of whole squares embraced by the area, and 
then estimate how many whole squares more are equivalent to 
the array of partially included squares along the boundary of 
the area. From the scale of the map calculate the area repre- 
sented by one square of the tracing paper, and thence derive the 
whole area of the figure in question. 

More elaborate methods involve the use of special instruments 
such as the planimeter. 

The "Amsler" planimeter is a beautiful instrument whose 
use is simple, but whose theory defies explanation in an 
elementary book. It consists essentially of an arm carrying 
a pointer which is moved round the boundary of the area to 
be measured, and a wheel which rolls on the surface of the 
paper. A second arm is pivoted to the first between the 
pointer and the wheel, and its other end is free to turn about 
a fixed point. As the pointer moves round the boundary the 
wheel revolves, sometimes forwards, and sometimes backwards. 
The nett amount of rotation forwards is measured by a revolu- 
tion counter and by divisions on the drum attached to the 
wheel. The nett rotation, multiplied by a suitable constant, 
gives the area. (See Plate X.) 

The precise computation of areas is an important part of the 
work of a cadastral survey, but its methods are beyond the scope 
of this book. 

Measurement of distances on a map. 

As in the measurement of areas, it is first necessary to know 
if the distances are correctly represented on the projection which 
is employed. And a treatment of this matter is beyond the 
scope of the present book. On all topographical maps the 
distances are shown so nearly true that they may be measured 
to within the error caused by paper shrinkage. For the methods 
of construction of scales see page 13. 



MAPS 35 



Map Reproduction. 



It would be impossible within the scope of this book to 
describe in detail the many processes which are employed in 
the engraving and printing of maps. But a very slight sketch 
of the principal methods may be of interest. 

The best of the old maps, in black only, were engraved on 
copper, and from the copper a steel-faced electrotype was made. 
The whole plate was covered with ink, and the surface wiped, 
leaving the engraved lines charged as in the ordinary process 
of printing from steel engraving. The print was made in a 
heavy press, which forced the paper into the engraved lines, 
from which they took up the ink. Maps printed from engraved 
plates can be distinguished by the relief of the lines. This 
process gives the best results, but it is slow and expensive, 
and does not lend itself to printing in many colours, which 
is now a necessity. In the production of modern maps, there- 
fore, the various processes of photolithography on stone or zinc 
have displaced printing from engraved plates. 

Where, however, the expense of engraving on copper can be 
afforded, an engraved plate still forms the basis of the process. 
P>om the engraved plate a print in light blue is taken, and the 
draughtsman inks in on this the portions which it is desired to 
print in any one colour. When this drawing is photographed 
the light blue disappears, and only the inked-in portion is 
transferred to the stone or zinc from" which the coloured im- 
pression is made. Thus it is possible to prepare from the 
basis of an engraved original as many colour plates as may 
be required. 

Recent improvements in colour printing presses have greatly 
increased both the speed and the accuracy of register of the 
impressions, so that it is possible to produce at a reasonable 
cost maps with a dozen or more impressions. The success of 
modern topographical maps is due largely to the greatly ex- 
tended possibilities afforded by these processes. 

Engraving on copper is costly, and many attempts have 
been made to find a substitute for it ; the engraving of the 
names, in particular, seems at first sight to be very wasteful. 

3—2 



36 MAPS 

But no method of stamping the names from steel dies has 
proved satisfactory. Some excellent results have been obtained, 
however, by drawing with a graver on glass coated with a white 
pigment which can be blackened chemically, and from which 
the printing plates can be made by photography. Another 
process which has given good results involves drawing on an 
enlarged scale on tracing paper, and photo-etching on copper 
from the drawing. But in each case the names have to be 
drawn — a tedious process. 

All these are for maps of the highest class. For cheaper 
work there is a variety of processes of photozincography, and 
of preparing zinc plates by contact printing from a tracing. 
For rapid work in the field on active service, field lithographic 
presses have been designed, and a Printing Company, R.E., 
accompanies the Intelligence Division on service, ready to re- 
produce in short time any plans, enlargements, or sketches that 
may be required. For an interesting account of the equipment 
and organisation of such a company, reference may be made to 
the Textbook of Topographical Surveying. 

For a complete technical treatise on the methods of engraving 
and printing, reference may be made to Methods and Processes 
adopted for Prodactioit of the Maps of the Ordnance SiLrvey, 
Second Edition, 1902. 



CHAPTER II 

MAP ANALYSIS 

Ordnance Survey Maps. 

Until within comparatively recent years the Ordnance 
Survey produced excellent maps but appeared to have little 
interest in the question whether they sold or not. The maps 
were published in the form of flat sheets only, and before they 
could be used out of doors it was necessary to spend at least as 
much as the price of the map in having it mounted on linen 
and put into covers. The means of distribution and sale of the 
maps were also very inadequate. 

About fifteen years ago maps mounted on linen and folded 
in covers were put on sale, and more recently the method of 
mounting in book form was introduced. This last simple ex- 
pedient has done more than anything else to increase the 
convenience of using the map, yet strangely enough it has 
not been imitated, and it is still difficult to get an unofficial 
map-mounter to understand how to do it. A map so mounted 
can be opened at any desired section with one hand, while the 
other hand remains free for driving or bicycling. The map does 
not catch the wind, nor does it offer much surface to the rain, 
and it can be consulted without attracting attention. 

It is a mistake to buy for field use any maps but those so 
mounted on linen, and folded without dissection. The dissected 
map is more flexible and lasts longer ; but it is impossible to 
make measurements upon a dissected map, and this should be 
sufficient to condemn it. 

Ordnance Survey maps can be bought at the local agents, 
and at the principal booksellers and railway bookstalls. It is 



38 MAP ANALYSIS 

not so well known that they can be obtained also by return 
of post from the Ordnance Survey Office at Southampton ; and 
this is very useful when a map is suddenly required while on a 
holiday. 

The large scale cadastral maps on the scales of 1/2500 and 
1/10,560 and the town plans of five and ten feet to the mile 
hardly concern us here. 

The topographical maps are 

the 1/63,360, or one inch to the mile, which is the standard topo- 
graphical map of the country, and in its recent form on large sheets is 
the most valuable for local use^ 

the 1/126,720, or half inch map, which is the standard military map 
for war and manoeuvres, and is also the most generally useful for motoring 
and bicycling. 

the 1/253,440, or quarter inch map, which is the most useful for 
planning long distance journeys, and for intelligent railway travelling. 

The smaller scale maps, ten miles to the inch, and the one 
in a million map, are for strategical and general purposes. 

The student should make a point of analysing examples of 
the different series, since in no other way is it possible to obtain 
an idea of the possibilities of the different scales, or of the 
difficulty of finding a uniform system of mapping that shall 
be satisfactory in all varieties of country. The following notes 
on selected sheets are given merely as illustrations of some of 
the more obvious points of interest. 

Ordnance Survey of England and Wales. 1/63,360. 

Sheet 42. (Large sheet series.) Third Edition. Llandudno. 

Printed in colour at the Ordnance Survey Office, Southampton. Dated 
1909. 

Relief by contours and hachures. Contours at 50, 100, and each 100 to 
1000, then at 250 feet interval to 3000. Printed in red, figured in black. 
The break in the contour interval at 1000 feet has particularly noticeable 
results on this sheet. 

Vertical hachures in brown; cliff drawing in black, very conspicuous. 
Spot heights frequent. 

^ This map can be obtained in the coloured edition, which is far the best (see 
Plate IV), and in the outline edition in black. The editions with hills in black and 
in brown have now been withdrawn. 



MAP ANALYSIS 39 

Contours in the sea bed 25 and ^ofeet below mean sea level, not fatho7ns 
as on the half inch map. 

Metalled roads: first and second grades, black filled yellow; third grade, 
thin double black. Unmetalled roads same, but narrower. Footpaths long- 
dotted, and very likely to be confused with parish boundaries. 

Woods, tree signs in black, over printed heavy green with boundaries. 

Margin divided into two-inch divisions, not carried across sheet, but 
lettered and numbered. No indication whatever of latitudes and longi- 
tudes, a grave omission. 

Small characteristic sheet attached. 

This sheet is a very good example of the present one inch map of Great 
Britain. 

Ordnance Survey of England and Wales. 1/126,720. 
Sheet 39. (Large sheet series.) Brighton. 

Printed in colour at the Ordnance Survey Office, Southampton. Dated 
1908. 

Relief by contours, hill shading, and layers. Contours at 50, 100, 200,... 
and by 100 feet interval to 1000; printed in brown, very lightly, and figured. 
Spot heights. Layer colours change at each contour, green passing through 
light brown to very heavy brownish green. Vertical hill-shading. The 
relief of the country is well shown, but underlying detail is obscured by 
the heavier colours, and the contours are confused by the hill-shade and the 
tree signs. 

Roads : black filled yellow, two grades, and inferior roads double black 
only. No tracks or hill paths. Water blue. No contours in sea. Woods 
green tree signs, no boundaries ^ 

Scale of miles. Latitude and longitude in margin, not carried across. 
Magnetic meridian and annual variation. 

Names black, stamped and ugly. 

Small characteristic sheet. 

The same: new edition. 1911. 

New scale of layer colours, changing at 100, 200,... 700, 800, 1000, green, 
through yellow, to pale brown. No hill-shading. The map is much more 
legible, but the strong effect of relief is lost. 

Contours in sea bottom: low tide, 5 and 10 fathoms. Layer tints of blue. 

Ordnance Survey of England and Wales. 1/126,720. 
Sheet 5. (Large sheet series.) The Lake District, 

Printed in colour at the Ordnance Survey Office, Southampton. Dated 
1908. 

Relief by contours, layers, and some hill-shading. 

^ Note : On some sheets of this edition the woods are shown by plain green tint 
without tree signs, e.g. Sheet 24, Huntingdon. 



40 MAP ANALYSIS 

Contours 50, 100, 200,... 1000, 1250, 1500, 1750, 2000, 2500, 3000, lightly 
printed in brown and figured. Layer colours change at each contour, green 
into pale brown, ascending to brownish grey, descending to bluish grey, 
ascending to dark slate colour. An exceedingly ugly map, showing the 
layer system at its worst. 

Other details as in Sheet 39 above. 

Ordnance Survey of Scotland. 1/126,720. 
Sheet 32. The Border Country. 

Printed in colour at the Ordnance Survey Office, Southampton. Dated 
1910. 

Relief by contours and layers. Contours 50, 100, 200, and at 100 feet 
interval right up, printed in brown, and figured. Spot heights frequent. 
Layer colours change at 100, 200, 300,... 800, 1000, 1500, 2000, 3000, green, 
yellow, leading to brown, and finally to an ugly shade of magenta (on the 
map), not conforming with colour scale in margin. No hill-shading. This 
colour scale adopted after the breakdown of the English scale on high 
ground. Result on this sheet unsatisfactory : colour uniformly heavy, 
obscuring contours. 

Roads : double black filled with yellow (two grades), and inferior roads 
double black only. Tracks and hill paths not shown. Water blue. Woods : 
green tree signs, no boundaries. 

Scale of miles. Latitude and longitude on margin, not carried across. 
Magnetic meridian and annual variation. 

Trans-border country shown fully (a welcome improvement in British 
practice). 

Names black : stamped and ugly. 

Small characteristic sheet. 

Ordnance Survey of Ireland. 1/126,720. 
Sheet 3. Donegal. 

Printed at the Ordnance Survey Ofiice, Southampton. Dated 191 1. 

Relief by contours and hill-shading. Contours uniformly at 100 feet 
interval throughout, printed lightly in red, and figured in brown. Hill- 
shading vertical. Spot heights. 5 and 10 fathom contours in sea, and 
blue layers. Woods green, with black tree signs and boundaries. 

Sheet divided into two inch squares, with reference letters and numbers 
in margin. 

Other characteristics as on the British sheets of this scale. 

The same, with layer colouring instead of hill-shading: see Plate V for 
small example. 

The new scale of tints is very successful. The series begins with two 
descending shades of pale green ; from 200 to 400 is left almost white, which 
is a new idea in layer colouring ; above 400 the successively increasing clear 
brown tints change at every 200 feet. This is by far the best layer map 
yet produced by the Ordnance Survey. 



MAP ANALYSIS 41 

Ordnance Survey of England and Wales. 1/253,440. 

Sheets 19 and 23 combined. Second Edition. Berks, Wilts, Hants, etc. 

Printed in colour at the Ordnance Survey Office, Southampton. Dated 
1911. 

Relief by hill-shading in brown. Spot heights. No contours. 

Roads : first class, black filled yellow ; second class, double black ; third 
class, single black line. 

Woods : tree signs in black, over printed pale green with boundaries. 

Margin divided in latitude and longitude, and meridians at 20' interval, 
parallels at 30' interval carried across the sheet. Notice the obliquity to the 
meridian of the sheet edges. 

The second edition differs from the original edition in the following 
points : The names are re-engraved and much improved ; the woods have 
tree signs added, and the colour is much paler ; the sign for railway station 
is much improved. 



Maps of the Geographical Section, General Staff. 

The Geographical Section of the General Staff, War Office, 
publishes a very large and varied selection of maps of British 
territories, and of other parts of the world in which Great Britain 
has special interests, or for which it is not likely that maps will 
be made by the local governments. 

Some of these maps represent the work of the Colonial 
Survey Section ; others are compilations from route traverses 
and miscellaneous work, and are of a provisional character ; 
others, again, as the map of Canada now in progress, are 
published by arrangement with the Dominion authorities. The 
series of maps of Turkey in Europe, and of China, cover regions 
which have not been mapped by the local authorities, while the 
maps of Arabia, Mesopotamia, and Persia provide material for 
the consideration of strategic and political interests. 

The style of production of these sheets is varied, and many 
of them, being provisional, are comparatively rough. Of recent 
years, and especially since the building of the new War Office 
gave the Geographical Section adequate accommodation, great 
improvements have been made in the execution of the maps, 
and the latest productions, particularly the Canadian map, and 
the first sheets of the International Map, are of the highest 
class. 



42 MAP ANALYSIS 

The following notes are intended only to call attention to 
the importance of a study of these maps for all students of 
geography. 

Orange River Colony. 1/125,000. 
Sheet 125. V. iv. Odendaal's Rust. 

Lithographed at the War Office, 1906. 

Relief by contours, in brown, at 100 feet vertical interval, and occasional 
hill-shading. Spot heights plentiful. 

Roads shown in three grades, principal roads filled yellow. Water blue. 
Bush shown by green tree signs. 

Margins show latitude and longitude, and index numbers and letters. 
Magnetic meridian and variation. 

Full characteristic sheet, and index to character of the river drifts, and 
of the water, grazing, and fuel at various halting places. 

There is little detail to be shown on the sheet, leaving room for notes on 
roads and character of country. 

Basutoland. 1/250,000. 

N.E. Sheet. (See Plate VI.) 

Printed and published by Geographical Section, General Staff. June, 
191 1. 

Relief by approximate contours, at 100 feet vertical interval, printed in 
brown. Cliff drawing brown. The contours are figured occasionally, but 
generally they are too close for figuring. 

Roads practically none. Bridle paths dotted black. Water blue. 

A very interesting example of the ability of contours to show the relief of 
a mountainous and difficult country where there are few names and no roads 
or other detail to break up the run of the contour lines. 

Uganda. 1/250,000. 

_, North A. 36 , . 

Sheet = (reference number on the new International Map system). 

Printed in colour and published by the Geographical Section, General 
Staff. 191 1. 

Relief shown by approximate contours at 200 feet vertical interval, with 
interpolated contours at 100 feet interval long-dotted. Contours drawn 
exceedingly fine and printed in pale brown. Spot heights very numerous, 
brown. 

Main roads coloured brown. Water blue. Forest by green tree signs. 
Cultivation yellow. Names very numerous, in black. 

Full characteristic sheet. Magnetic meridian. 

An unsatisfactory map, the relief of the ground quite illegible, owing 
to the confusion of the very faint contours with other detail. It should be 
compared with the map of Basutoland produced in the same year in the 
same office. 



Plate VI 




Geo*/r<iphicaLSec^L(jfi^, GenetyxlSiijfr 



MirOtrioeJS/S 



PART OF N.E. SHEET 

BASUTOLAND 
Scale — 250,000 



FORM LINES AT APPROXIMATE 100 FT. V.I. 



Plate YE. 



P UIU> SHVCyKHOVSKY 

II MintakaP. , 

4^ ^KhunjerakP. 

. ^ 18900 



A CJI AR ^3300- -~>r^^^ 

2*270 Mustagnr.,, __. • ~^ V^^ 








CeoorapIikjuxLSectLon', Genjcfdb'Stij^ 

PART OF SHEET 

PERSIA AND AFGHANISTAN 
Scale - -s.oss.o^o 

NEW EDITION 1913. 



W^ Office lifts. 



MAP ANALYSIS 43 

Persia and Afghanistan. 1/4,055,040. 

Published by the Geographical Section, General Staff, War Office. 1906. 

Relief by contours and layer system. Contours at 500, 1000, 2000, 
4000, 6000, 8000, loooo, 15000, and 20000 feet, printed in brown, not figured. 
Layer colours in increasing shades of brown, changing at the above contours. 
No spot heights. 

Railways in red, with distinction of gauge. 

Roads in red. Water in blue. 

Meridians and parallels at 5° interval carried across the sheet. 

International boundaries green. 

An interesting example of the difficulty of representing the tremendous 
mountain region of the Indian N.W. Frontier. Even with the great vertical 
interval of 5000 feet the contours in many places are too close for a clear 
appreciation of the layer tints. 

A new edition of this map is in preparation, which is a great improvement 
on the old, and has many features of interest. The system of layer tints, 
green through orange (of a brownish shade) to clear red, is light and clean. 
There is some hill-shading in greenish ray, and contours are in grey. 

We are much indebted to the Chief of the Geographical Section, General 
Staff, for placing at our disposal the specimen of the new edition given on 
Plate VII. 

Foreign Maps. 

Nearly all the countries of Europe are now more or less 
completely mapped, and the publications of the respective 
Survey Departments exhibit every variety of style, and of 
success or comparative failure. In other continents the work 
of survey is naturally less advanced ; but there are now few 
civilised states which have not realised the importance of an 
accurate survey of their territories. 

Within the limits of this small book it is impossible to do 
more than make notes on some of the interesting characteristics 
of a selection of foreign topographical maps. It is hoped that 
the selection is fairly representative, but it is far from complete, 
and the specimens chosen for annotation are doubtless not 
always the best. The author is, however, so convinced of the 
importance of a study of these foreign maps that he has thought 
it best to give in all cases the number of the sheet to which 
these brief notes refer, in order that students may have some 
guide in purchasing examples of the work of the principal 
foreign surveys. 



44 MAP ANALYSIS 

Since the object of this study of various examples is to 
compare the respective merits of different systems, it is inevitable 
that the question will arise, How do the British maps compare 
with those of other European countries ? The answer appears 
to be that there are isolated examples of topographical maps, 
new series of which only a few sheets have appeared, which are 
in some respects better than British maps : notably the 1/50,000 
map of France, and the 1/250,000 map of Bavaria. But on the 
other hand there is no country which has maps of greater variety 
and completeness, and of more uniform excellence. 

France. 1/50,000. 

Sheet XXII. 14. Versailles. 

Not dated. Printed in colours by the Service Geographique de PArmee. 

Relief: contours and double system of hill-shading. Contours in brown 
at 10 m. vertical interval, but not figured. Spot heights frequent. Vertical 
hill-shade in bistre ; oblique shade from north-west in purplish grey. 

Roads in black, four grades ; tracks in black, two grades. 

Buildings in red, so that where a road approaches a town and becomes 
bordered with houses it loses its black outline and becomes less conspicuous. 
Water blue. 

Scale of kilometres. Latitudes and longitudes shown on margin in the 
ordinary and the centesimal division. Origin of longitudes Paris. Meridians 
and parallels not carried across the sheet. 

Woods, meadows, and gardens in different shades of green ; orchards 
and vineyards in purple, which becomes confused with the grey hill-shading 
and sometimes destroys its effect. 

Population of each village shown in red, but the date of census not 
shown. 

An excellent feature is that the margins are left open, and the principal 
roads, railways, etc. are continued off the sheet, together with anything 
which would suffer from being cut across by the sheet margin. 

Railways, three grades, narrow gauge, and tramways, all in black. 

Writing very plain. Names of water in blue. 

Elaborate characteristic sheet, including separate signs for factories 
operated by steam, water power, and electricity respectively. 

The most elaborate topographical map yet produced. 

France. 1/200,000. 
Sheet 8, Abbeville. 

Printed in colour and published by the Service Geographiqice de VArmee. 
No date. 

Relief shown by contours and vertical hill-shading. Contours at 20 metres 



MAP ANALYSIS 45 

vertical interval, very finely drawn, printed in pale brown, and not figured. 
Hill-shading brown. 

Roads and tracks, six grades, in red. Railways in black. Water in 
blue. Woods in green ; tree signs. 

Meridians and parallels carried across map, inclined to margins, figured 
in centesimal division of the quadrant. Margin divided also in kilometres. 

Full characteristic sheet. 

The contours drawn so lightly and so much overlaid with names and 
detail that the relief is illegible. 

Bavaria. 1/100,000, 
Sheet 637. Landsberg. 

Published by the Bavarian General Staff. 1904. 

Relief by contours and hachures. Contours at 50 metres vertical interval, 
printed and figured in brown. Vertical hachures in brown. 

Roads in three grades, double and single black. 

Water blue. Woods by tree signs in black. 

Names of water sloped to left. 

Margin shows latitude and longitude (East of Ferro). 

Scale of kilometres and "geographical miles": one mile = 7420*44 metres. 

The contours drawn so lightly and so much overlaid with detail that 
relief illegible. 

Bavaria. 1/250,000. 

Sheet 8. Munich to southern frontier. 

Dated 1906. Printed in colours. K. Topograph. Bureau. 

Relief by contours, hill-shading, and layers. Contours at 100 m. 
interval throughout ; contours at boundaries of layer tints strengthened ; 
all printed in brown ; some intermediate contours in brown long-dotted. 
Contours not figured, and spot heights infrequent. Hill-shading light grey, 
oblique, north-west light. Layer colours in spectrum order, leading to very 
clear red for high mountains. Colours change at 300, 400, 500, 600, 800, 
1000, 1200, 1500, 2000, and 2500 m. 

Roads in black. Water in blue. Woods not shown. 

Scale of kilometres. Latitudes and longitudes on margin. Origin of 
longitudes not stated ; evidently Ferro. Meridians not carried across sheet. 

Trans-frontier country left nearly blank. 

Writing : pl9.ce names italic ; mountain names block ; water names in 
blue, sloped to left. 

No characteristic sheet attached. 

The general effect of this map is exceedingly good ; it is perhaps the 
best example of its kind. 

Saxony. 1/25,000. 

Sheet 15. Wellerswalde, 

Engraved, lithographed, and printed at Leipzig for the Saxon General 
Staff. 1906. 



46 MAP ANALYSIS 

Relief by contours, in brown, at 5 metre intervals, the intermediate 5's 
broken, and the 20's strengthened. Also subsidiary dotted contours when 
required, at variable intervals down to i m. Contours not figured, except in 
the margin, but spot heights numerous, and the contours easy to read on 
this sheet. 

Railways and roads black. Water blue. Woods by tree signs, black. 

Elaborate characteristic signs, but no explanation attached. 

Margin shows latitudes and longitudes (East of Ferro). 

A very well-engraved and clear sheet. 

Switzerland. 1/25,000. 
Sheet 376. Pilatus. 

Dated 1894. Revised to 1906. Printed in colour by the Eidg. Topograph. 
Bureau. 

Relief by contours in brown, at 10 m. vertical interval ; every tenth 
contour long-dotted and figured. The contours are so close that they are 
very hard to follow. Cliff drawing in black. 

Roads in black, of two grades. Tracks in black, long-dotted. 

Scale of kilometres, and map divided into squares of approximately 6 cm. 

Latitudes and longitudes shown on margin. Origin of longitudes not 
stated, apparently Paris. 

Meridians and parallels not carried across the sheet. 

Woods shown by very minute tree signs in black, making the pale brown 
contours still more difficult to read. Water blue. 

Writing in italic ; no distinction between physical features and village 
names. 

No characteristic sheet attached. 

Switzerland. 1/100,000. 

Sheet XVIII. Rhone Valley and Simplon. 

Dated 1854, revised to 1907. Engraved, and printed in black. 

Relief shown by hachures, darkened on the side away from a north- 
west oblique light. Good cliff drawing. Glaciers only contoured. Spot 
heights in metres, small and rather illegible. 

Trans-frontier country shown in full. 

Roads double black lines, white between, showing up well on the dark 
hachures. 

Tracks long-dotted, not very distinct. 

Scale of kilometres and hours. (One hour equals 4*8 km.) 

Latitudes and longitudes shown on margin in the ordinary and also in 
the centesimal system. Origin of longitudes not stated. Meridians not 
carried across the sheet. 

No characteristic sheet attached. 

Switzerland. 1/250,000. 
Special railway map. 

Published by the Swiss Topographical Bureau, Bern. 1908. 



MAP ANALYSIS 47 

The ordinary engraved and hachured map is printed in brown. Rail- 
ways with names of stations are heavily overprinted in black. 
An excellent example of the map for special purposes. 

Italy. 1/100,000. 
Sheet 32. Como. 

Dated 1907. Printed in colour at the Istituto Geografica Militare. 

Relief: contours and hill-shading. Contours in light brown, at 50 m. 
vertical interval. Hill-shade oblique, north-west light, brown. Frequent 
spot heights. Roads in black. Three grades metalled, two grades un- 
metalled, and various kinds of tracks distinguished. Railways, double and 
single, tramways narrow gauge and tramways distinguished. Water blue. 
Houses black. Woods not shown. 

Scale of kilometres. 

Latitudes and longitudes on margin. Origin of longitudes : Rome, 
Monte Mario. 

Meridians and parallels not carried across the sheet. 

Mountain names in engrossing. Water names in black. 

Good characteristic sheet attached. 

Italy. 1/200,000. 
Sheet II. Brescia. 

Dated 1908. Printed in colour, by the Istituto Geografica Militare. 

Relief by contours and hill-shading. Contours at 100 m. vertical interval. 
Hill-shade in grey brown, oblique. 

First and second grade roads in red ; third grade, black in the plains 
and red on the mountains. Minor roads made and unmade, muletracks, 
footpaths easy and difficult, and mountain passes all distinguished by 
characteristic signs. Railways black. Water blue. Towns by signs to 
indicate degree of importance. Double, single, narrow gauge, and tram- 
ways of various kinds, all distinguished by signs. Woods pale green. 

Scale of kilometres. 

Latitudes and longitudes shown on margin. Origin of longitude : Rome, 
Monte Mario. Meridians and parallels not carried across sheet. 

International frontier with broad band of colour. Trans-frontier country 
in full detail. 

Mountain names in engrossing, difficult to read. 

Good characteristic sheet attached. 

Central Europe. Austrian General Staff Map. 1/200,000. 
Sheet 41° 41°. Saloniki, 

Dated 1903, revised to 1909. Printed in colour. 

Relief by hill-shading and contours. Hill-shade vertical, pale brown. 
Contours darker brown, at 100 m. interval. 

Roads in black, two grades ; and tracks long-dotted. Railways black. 
Water blue, but not the names of water. Woods shown by pale wash of 
2-reen. 



48 MAP ANALYSIS 

Latitudes and longitudes on margin. Origin of longitudes : Ferro. 
Meridians and parallels not carried across sheet. Sheet not bounded by- 
meridians and parallels. 

Scale of kilometres and schritte. (looo schritte = 075 km.) 

Mountain names in engrossing. 

No adequate characteristic sheet attached. 

A very ugly map. 

Central Europe. Austrian General Staff Map. 1/750,000. 
Sheet 8. Skoplje. 

Dated 1900. Printed in colours. 

Relief by contours and layers. No hachures or hill-shading. Contours 
at 150, 300, 500, 700 and thence at 300 m. intervals; layer tints in ascending- 
shades of brown, rather heavy. Contours in darker brown are the boundaries 
of the layers ; no intermediate contours. " Thalsohlen und Thalebenen," 
apparently plains in the bottoms of valleys, in two shades of greenish blue. 

Roads of two principal grades in red ; third grade in black ; tracks in 
black, long-dotted. Railways in black. Water, including names of water, 
in blue. 

Scale of kilometres. 

Latitudes and longitudes on margin. Origin of longitudes : Ferro. 
Meridians and parallels drawn across sheet. 

Woods not shown. Mountain names in engrossing. 

No characteristic sheet. 

Austria-Hungary. School district maps. 1/100,000. 
Sheet Deutsch-Lansberg. 

Dated 1910. Printed in colours by Freytag and Berndt, Vienna. 

Relief by contours, oblique hill-shading, and layers. Contours in brown 
at 50 m. vertical interval. Hill-shading in grey, by north-west light. Layer 
tints in pale green, yellow, orange, and red. Contours at 1000 and 2000 m. 
long-dotted. Colour changes at 400, 500, 700, and 1500 metres. Difiference 
of tints so slight, and so much obscured by hill-shading, that practically only 
the change at 500 from green to yellow is of much account. 

Roads in black, two grades ; no tracks shown. Railways in black. 
Water blue. 

Scale of kilometres. Section across the country. 

Woods not shown. 

Latitudes and longitudes on margin. Origin of longitudes : Greenwich. 
Meridians and parallels not carried across the sheet. 

Writing: no distinction between place-names and physical features. 

Characteristic sheet attached. 

Price 50 heller (about 5^.). Very good maps for the price. 

Greece. 1/75,000. 

Sheet 40° 1° E. PA^ANH-TEMnH. 

Dated 1909. Printed in colours by the K. K. Geog. Inst., Vienna. 



MAP ANALYSIS 49 

Relief by vertical grey shading. Contours at 20 m. darker grey ; 100 m. 
contours strengthened ; occasional intermediate 10 m. contours long-dotted. 
Sea bottom contoured, at 2, 5, 10, and by tens to 60 m. Cliff drawing 
brown. 

Principal features across frontier shown, with 100 m. contours and hill- 
shade. 

Roads red, in three or more grades. Tracks in red. Water blue. 
Woods black, with tree signs. 

Scale of kilometres and Bemata (paces). Scales of slopes corresponding 
to contour intervals (this an unusual feature). 

Latitudes and longitudes on margin. Origin of longitudes : Athens, with 
reduction to Greenwich. Meridians not carried across sheet. 

Writing in modern Greek character. Mountain names engrossing. 

Complete and elaborate characteristic sheet attached. 

Sweden. 1/200,000, 
Sheet 58. Kolasen. 

Date 1905. Printed in black and slight colour. 

Relief by hachures below about 550 metres and contours above; both 
black. Hachures vertical; contours shaded to bring up relief, apparently 
arbitrarily. Contours not figured, and spot heights insufficient to show 
contour interval. Combination of hachures and contours in this way unusual. 

Principal roads double black line, yellow between. Lakes blue. Rivers 
black. 

Scale of kilometres. 

Latitudes and longitudes on margin. Origin of longitudes : Stockholm, 
with reduction to Greenwich. Meridians but not parallels carried across 
sheet. 

Woods not shown very clearly; small black tree signs on the hachures 
hardly distinguishable. 
■ Trans-frontier country left entirely, blank. 

Writing : no distinction between hill names and villages ; names of lakes 
sloped to the left. 

No characteristic sheet attached. 

Sweden. 1/500,000. 
Sheet II. 

Date 1896. Printed in colour by the Swedish General Staff. 

Relief by contours and layers. Contours at 100 metres vertical interval, 
in brown, with intermediate contours at 33 and 66 metres up to 500 metres. 
Layers changing tint at each 100 metres, in shades of yellow, brown, bluish 
grey, to white. Colour scale ascending, then descending. No hachures or 
hill-shading. 

Latitudes and longitudes shown on the margin. Origin of longitudes : 
Stockholm. Meridians and parallels carried across the sheet. Edges of 
sheet not meridians but much inclined. 

H. M. s. 4 



so MAP ANALYSIS 

Lakes blue ; rivers black. No roads on this sheet. Woods not shown. 

Trans-frontier country left entirely blank. 

Writing all in black. River and lake names in character sloping to left. 

Mountains in separate character, but not engrossing. 

Scale of kilometres. No characteristic sheet attached. 

United States. 1/62,500. 
Glens Falls Sheet. 

Published by the United States Geological Survey. 1906. 

Relief by contours, printed in brown at vertical interval 20 feet ; every 
fifth strengthened, and every fifth or tenth figured. Occasional spot heights 
in brown. 

Roads and railways black. Water blue. 

Meridians and parallels carried across sheet. Longitudes from Greenwich. 

The representation of the relief by contours very successful, depending 
largely on absence of names and other detail. 

Full explanation and conventional signs on back of sheet. 

The International Map on the scale of 1/1,000,000. 

At the international Geographical Congress which assembled 
at Berne in 1891 it was proposed by Professor Penck, then of 
Vienna, and now of Berlin, that steps should be taken to urge 
the publication of a map of the whole World on the scale of one 
in a million, with sheets uniform in size and shape, systematic- 
ally arranged, and drawn in uniform style. Such a series of 
maps would clearly help the comparative study of different 
regions of the World. 

At the next meeting of the Congress, held in London in 
1895, the proposal was discussed in detail, a number of reso- 
lutions were voted, and schemes for the division of the sheets 
and the methods of construction were adopted. Two preliminary 
difficulties had to be overcome. The choice of the initial meridian 
had to be made; and some means had to be found of reconciling 
the differences between metric and non-metric countries. 

As to the former, there could be little real difference of 
opinion, for the maps and charts whose longitudes are referred 
to the Greenwich meridian were greater in number than those 
referred to all other meridians together. The question of a unit 
of length was nearly unessential, because it would be easy to 
draw on the margin of the map scales expressed in as many 



MAP ANALYSIS 51 

units of length as might be desired. But the question whether 
heights should be expressed uniformly in metres was difficult, 
because the British delegates at that time refused to have any- 
thing to do with the metric system on British sheets. Eventually 
it was agreed to adopt the meridian of Greenwich as the prime 
meridian, and the other question was left undecided. 

For thirteen years little was heard of the scheme. The 
resolutions of the Congress bound no one ; and though several 
countries undertook the publication of maps on that scale, they 
did so independently and in ditTerent styles. This delay was 
useful in that it allowed the accumulation of experience in the 
use of this scale, which is intermediate between the scales 
ordinarily used for topographical maps and for atlas maps. 
And systems which give excellent results on one scale very 
often fail altogether on another. 

At last the question of the International Map was revived 
at the Congress held in 1908 at Geneva. More resolutions were 
voted, and there seemed every likelihood that they would remain 
as inoperative as those that had gone before, for the Congress 
that voted them was not in the position to undertake itself the 
construction of the map, and in default of an official agreement 
between the Governments interested, very little could be ex- 
pected. At this point the British Government resolved to take 
the steps necessary to put the project on an official basis, and 
issued invitations to the principal Governments of the World, 
to send delegates to a committee, which should discuss the 
question and make definite recommendations. This committee 
met in London on November 19, 1909, and speedily arrived 
unanimously at an agreement which was ratified by all the 
Governments concerned. The official report of the proceedings 
was published in February, 19 10; the following is a short sum- 
mary of the decisions. 

1. A uniform set of symbols and conventional signs was adopted, and 
a characteristic sheet prepared. 

2. Each sheet covers an area 4 degrees in latitude by 6 degrees in 
longitude ; but nearer the poles than latitude 60°, two or more sheets of 
the same zone may be joined. The limiting meridians are reckoned from 
Greenwich, and the limiting parallels from the equator. 

4—2 



52 MAP ANALYSIS 

3. The sheets are numbered according to a diagram attached to the 

Report on a plan which is somewhat compHcated. Each sheet has a 

number, such as 

North K. 35. 

The letter K signifies the zone of latitude 40° to 44°, the eleventh zone from 
the equator, as K is the eleventh letter of the alphabet. The number 35 
signifies the 35th lune of longitude, each of six degrees, reckoned eastward 
from the meridian opposite that of Greenwich. Thus a short calculation 
leads to the result that sheet North K. 35 is the sheet covering Latitude 
N. 40° to 44° and Longitude E. 24° to 30°. The merits of this system of 
numbering are not obvious. 

Each sheet must also bear the geographical coordinates, that is to say, 
the latitude and longitude of its central point ; and there seems to be no 
reason why these numbers should not have been used as the sheet numbers. 

4. The projection is a slightly modified form of the polyconic projection 
proposed by one of the French delegates, M. Lallemand. It has all the 
properties necessary for such a map ; that neighbouring sheets shall fit 
along their edges ; that the representation of distances and bearings within 
the sheet shall be sensibly perfect ; and that it shall be constructed with 
ease. 

The upper and lower parallels are constructed as in the ordinary poly- 
conic projection, but they are brought slightly closer together, so that the 
meridians 2° from the centre are their true lengths, instead of the central 
meridian ; and the meridians are drawn as straight lines instead of being 
slightly curved. These refinements on the ordinary polyconic projection 
are practically not detectable on the printed sheet, but are theoretically 
elegant. The tables necessary for the construction of the sheets are given 
in the Report ; they occupy only two pages. 

5. Contours are drawn at vertical intervals of 100 metres, "but in very 
hilly districts the contours may be at larger vertical intervals, provided that 
they are spaced at 200, 500, or 1000 metre intervals." The map is coloured 
on the layer system, according to a scheme attached to the Report, following 
the spectrum order of colours, except that an ugly shade of magenta is used 
instead of red. 

The tints are changed at the contours given in the following scheme : 

From sea level at every 100 metres to 600; 

thence at intervals of 200 metres to 1200; 

thence by two steps of 400 metres to 2000 ; 

thence by two steps of 500 metres to 3000 ; 

thence by steps of 1000 metres to 7000. 
It is not made clear whether the contours should be shown uniformly at 
intervals of 100 metres, irrespective of the changes of tint; but it may be 



MAP ANALYSIS 53 

noticed that steps of 400 metres are specified in the colour scheme, whereas 
they are excluded in the specification for the contours which immediately 
precedes. 

6. Minor features of importance, which would not be shown by the 
contouring, may be represented by shading, but not by hachuring ; and 
the method of lighting which is most effective for the district may be 
selected. 

Thus there is liberty in hill-shading, but not in contouring. 

7. Precise rules are laid down for the spelling and transliteration of 
place-names. The basis of these rules is that the spelling of every place- 
name in an independent country or self-governing dominion shall be that 
adopted by the country or dominion. This is of great importance, since it 
abolishes the customary corruptions of place-names as used by foreigners in 
such countries as Turkey. 

8. Water features and glaciers are in blue ; contours in brown, for the 
land, and in blue for the sea bottom; roads are in red, and railways in 
black. 

9. Heights above mean sea level are in metres, mean sea level being 
deduced in each country from tidal observations on its own coasts. 

These are the principal resolutions in the Report of the 
International Map Committee. How far they can be put into 
practice uniformly cannot be predicted. The few sheets which 
have appeared at the time of writing have already shown some 
not unimportant deviations from the strict letter of the scheme, 
which are noted in the brief analyses which follow. Doubtless 
there are excellent reasons for each departure from the strict 
rule. Nevertheless it seems to the writer that it would have 
been better to make the first few sheets in strict conformity 
with the resolutions of the Committee, because it would then 
have been easier to see how far it is necessary to give greater 
latitude in the application of these rules. 

The International Map was necessarily an experiment, be- 
cause the Committee which drew up the Convention for its 
execution had not before it any example of a map on that 
scale elaborately printed in colour ; none had been produced at 
that time. This being so, we are not bound to consider the 
existing scheme as fixed for better or worse, and it is legitimate 
to discuss what improvements are possible. 



54 MAP ANALYSIS 

But let us first note any special points in the sheets already 
published. 

International Map. 1/1,000,000. 

Sheet North O. 30. Scotland. The Highlands. 

Published by the Ordnance Survey. 1912. 

The following variations from the Conventional signs sheet may be 
noticed. 

Above 200 metres the contour interval is 200, instead of 100. This 
deranges the layer tints, whereby one tint of green and both of yellow are 
lost. 

No hill paths are shown. 

The coast line is drawn as a sea-contour (blue) instead of as a land- 
contour (brown). This gives a weak effect to the islands. 

In spite of the increased vertical interval the contours in the mountains 
come so close together that the layer system loses effect. 

International Map. 1/1,000,000. 
Sheet North M. 31. Paris. 

Published by the Service Geographique de PAnne'e. 191 1. 

Although the country is generally of sHght elevation, only the 100 metre 
contours are shown, and the representation of relief is therefore very 
inadequate. 

The colours do not follow the adopted scale very closely, and in 
particular the blue is bad. 

The compilation of the part of Holland shown has mistakes in spelling, 
and the main stream of the Rhine through Dordrecht and Rotterdam is not 
shown as navigable. Hook of Holland, Flushing, Queenborough, and New- 
haven are not shown as ports with regular mail service. 

International Map, 1/1,000,000. 

Sheet North K. 35. Istambul. (See Plate VI.) 

Printed and published by the Geographical Section, General Staff. 191 2. 

The following variations from the Conventional signs sheet may be 
noted : 

The lower contours are at intervals of 200 metres. 

This disarranges the layer tints. Green goes to 400 instead of 300, and 
there is only one tint of yellow. 

The blue of the sea below the 200 metre contour is very intense, and this 
gives a weak appearance to the coast line, which might perhaps have been 
avoided if the coast line had been drawn in brown as a land contour. 

The names — which are the real names of the places, and not the con- 
ventional Anglicized forms — make a very interesting study, and there is 
a valuable glossary of pronunciation of Bulgarian, Rumanian, and Turkish. 

This sheet is a beautiful example of the merits of the style of lettering 
adopted for the International Map. 



Plate Ynr. 




GeoyraphxcaL Se'-tian,, GeneraiLStafr 



Wiir Office 1913 



INTERNATIONAL MAP OF THE WORLD 
Scale — 1,000,000 

PART OF SHEET "nORTH K 35 ISTAMBUL" 



Plate JX. 






r- {.^^m-^M ; ,^ \ Vim 



IP KOPJES 



-5 

Tergpla > liiy \l ^ 



■;i\ -■';"' 



r 



>Koooocff Af¥ '/ 

^1 .p'Wya^oorii. V ' 

, 'jBannetaE^t 










j^t) ^>!i v ;;,-•. 1 p^-TMg'^L' Hotter' 



a« 



3uT 




cob's I 



imteia^^ 



t •' "° - ^i~* ■ ^ ° 

J^ -(feMobsSbiiteiix / ^ 



KbelEai 



XI 



Spoe< 
oogevDet 9 



/■'■' ^^^-'- ■ I&ruisPaJ. K ]■ 



Elandsfenteir? 



?B aiikaByirtem. 



Maze! 
Flona&HtexT 




GeoffraphicaJ Se^tji/n. OfTter-a/ Staff 



Wiir0frUxl9l3 



INTERNATIONAL MAP OF THE WORLD 
Scale — j,ooo,ooo 

PART OF SHEET "sOUTH H 34^ KENHARDT" 



MAP ANALYSIS 55 

International Map. 1/1,000,000. 

Sheet South H. 34. Kenhardt, Cape Colony. (See Plate VI.) 

Printed and published by the Geographical Section, General Staff. 191 1. 

This sheet follows very closely the Conventional signs sheet of the 
International Committee. 

Contours are shown at uniform intervals of 100 metres, but are not 
carried across the frontier into German South-West Africa. 

The ground rises steeply from' the sea to 1000 metres, and the greater 
part of the sheet is heavily coloured brown. A good example of the failure 
of the layer system on high plateaux. 

The impression to be derived from a study of these first 
sheets is, that in most respects they are very successful, but 
that in the most important of all, the representation of relief, 
they are not entirely satisfactory. 

The style of the lettering serves admirably to distinguish 
between features of different kinds by differences in the character 
of the letters. Physical features are perfectly distinguished from 
names of towns, and both are equally legible. The systematic 
transliteration of the place-names, and the glossaries of pronun- 
ciation of the Slavonic names, are features of great value. The 
indication of the population of a town by its characteristic sign 
is good, and so is the retention of the real name of the town in 
place of the name by which it is habitually known in other 
countries. 

The hard and fast rules for the boundaries of the sheets work 
badly in Scotland, where the six degrees of longitude assigned 
as the width of the sheet are diminished by the convergence of 
the meridians so that the sheet is nearly half as tall again as it 
is broad. It would have been more convenient to extend the 
sheet westward to include the Hebrides, which by the rule must 
be shown on the eastern edge of a separate sheet. North of 
latitude 60° the sheets are doubled in width, so that the 
Shetlands will have to themselves a sheet nearly double the 
width of the Scotch and English sheets. 

The result of the first application of the layer system to the 
scale of one in a million is not encouraging. The wide vertical 
interval of the contours on the lower ground — 100 metres — is 
too coarse for the effective representation of the lower land ; 
while the small horizontal distance between the contours in the 



S6 MAP ANALYSIS 

more mountainous country, due to the small scale of the map, 
makes the interlacing of the layer tints too complex for a clean 
result. The mingling of very narrow strips of various tints 
produces only a quiet ineffectual colour, in the same way that 
brilliant coloured threads are blended into a tweed of the most 
unobtrusive kind. A strip of layer tint must be at least five 
millimetres broad if it is to have size enough to develop its 
effect ; but this principle was not recognised when it was resolved 
to construct the International Map upon the layer system. 

It is understood that the Ordnance Survey will publish an 
edition of the British 1/1,000,000 sheets without the layer colours. 
That will give an occasion to try whether there is not a simpler 
plan of achieving the desired effect. It appears to the author 
that on maps of the small scale of one in a million it would be 
possible to obtain all the effect of relief required in mountainous 
regions by printing the simple contours in colours chosen after 
the plan of the layer system of tints. But it must be confessed 
that no one in command of a map office, and in the position to 
make a trial of this notion, has ever shown much inclination to 
adopt it. 

Aero maps. 

The rapid advance of flying two years ago produced a sudden 
demand for maps of a new kind, in which some attempt should 
be made to depict the country as it appears from above, and 
especially to emphasize the objects which serve as leading marks 
to the pilot in charge of the aircraft. Experimental maps were 
produced by the General Staffs of Great Britain and of France, 
by the Aero-Club de France, and by the promoters of the great 
flying " circuits " which had a brief success. 

At the meeting of the British Association held at Portsmouth 
in 191 1 there was an interesting discussion on aero maps, and 
strong divergences of opinion were manifested. The military 
flying men were not pleased with the special maps, and declared 
that the ordinary half inch or quarter inch maps, though not 
perfect, were better than any others. The civilians complained 
that they needed something more simple and easy to read 
than the Survey maps. But it was pointed out that the onl}' 



MAP ANALYSIS 57 

competitor in the Circuit of Britain who never lost his way was 
the French naval officer who flew over ground with which he 
was quite unacquainted by the aid of the quarter inch map ; 
and that all who relied upon the route maps specially prepared 
for them had come to grief. 

The special maps prepared by the General Staffs showed the 
roads white, as it was imagined that they would look from above. 
But just at that time the main roads were extensively tarred, 
and thus they lost their whiteness, and became less conspicuous 
from above than the secondary roads. Moreover, it was found 
that the appearance of the ground below changed so greatly 
with the change of light that the attempt to imitate it to some 
extent is doomed to failure. 

If special maps are to be made in the future, it seems likely 
that the most useful modification will be to accentuate the 
characteristic shapes of road junctions and crossings. On the 
ordinary maps these are generally masked by the exaggerated 
conventional width of the road. But it should not be difficult 
to exaggerate also the special shape of the crossing which is 
often perfectly characteristic, and thus to make use of the 
natural signs which much exceed in size and distinctness any 
that could be erected for the special purpose of acting as 
guides to flying. 

The whole subject is hardly as yet in the experimental stage, 
however, and the information gathered in the manoeuvres of 191 2 
is not at present available. 

The following notes on the special maps issued in 191 1 may 
be of interest. 

England. Aero map of the igii MancEuvre Area. 1/253,440. 
East Anglia. 

Printed at the War Office. 191 1. In colour. 

General groundwork of the sheet greenish grey. 

Coarse vertical hill-shading. Spot heights in feet. 

Roads in white ; two grades. Water blue. Towns red. 

Woods in green. Parks in very pale green. Churches with spires (but 
not those with towers), windmills, and isolated trees in black. 

Railways in very heavy double or single black. 

It is believed that this map was not considered a success by the military 
aviators. 



58 MAP ANALYSIS 

France. Carte Aeronautique. 1/200,000. 
Sheet: Chalons. 

Printed in colour and published by the Service Geographique de V Ariiiee. 
Paris. [191 1.] 

The ground of the map is grey. Relief is shown by vertical hill-shading 
in brown. Spot heights. 

Woods in uniform tint of bright green. Water blue. 

Roads are white between black lines. Villages in red. 

Railways in black, three grades. 

Ground dangerous for landing hatched in red. 

Special characteristic signs for hangars, landing grounds, and hydrogen 
depots ; cathedi'als, chateaux, factory chimneys ; high tension electric cables, 
etc. 

An interesting example of special map, rather heavy and dull in colour. 

Carte de I'Aero-Club de France. 1/200,000. 
Sheet 93. Laon. 

Printed in colour and published by Ed. Blondel la Rougery. Paris. 
No date. 

Relief by rough grey vertical hill-shading. Spot heights, summits 
distinguished. 

Railways black, grades distinguished. Roads double black line, principal 
roads filled red. 

Water blue. Woods plain green tint. 

A large variety of special characteristic signs, of importance to aviators : 
aerodromes, landing grounds, hangars, hydrogen factories, gas works, etc. 
Sketches of the principal buildings in the margin. 

A crudely executed but interesting attempt to provide the special 
information required by aircraft. 



Plate X 




I. The Amsler Planimeter. 





^mm 


(*s^^^r^ 




iiPsn-^1 




w 


w^ - 




^v...... 


7 




*y 


p^ 












'a 


R A S 


T r 


// /; 


,v 


T 


/: 


/.' 


J. 






1 <" / /■ .V 










^ 



2. Central parts of planimeter (from above). 



Measureinetit of Areas. 



CHAPTER III 

route traversing 
The Explorer's Route Map 

The object of the Route Map. 

The first care of a traveller who passes through an unknown, 
or but partially explored, country is to make a record of where 
he has been, and of the main features of the country along the 
route by which he has travelled. Often singlehanded, encum- 
bered by transport, compelled to keep to the track, and unable 
to leave his party, he cannot hope to make anything in the 
nature of a map, in the ordinary sense of the term. But for his 
own guidance, to avoid getting lost, he is compelled to determine 
his position day by day in much the same way that the position 
of a ship is determined at sea, by observation of the Sun and 
the stars, so that he is able to say roughly in what latitude, and 
perhaps in what longitude his halting places were. Moreover, 
as he goes along he is able to make such observations of the 
shape and course of his path as to enable another man coming 
after him not only to arrive more or less at the same place, but 
to follow the same route. And finally, he can keep a sort of 
running record of the things that lie immediately to the side of 
his path. All this he does by the construction of a "route 
traverse " or " route map." 

It is essentially the work of the pioneer, whose main business 
is to get through the country, and who can afford to give to 
mapping and survey only a small part of his attention, and 
no voice in the determination of his plans. Such is the first 
exploratory survey of a country. Route traverses were run 



6o ROUTE TRAVERSING 

across Africa by the explorers of last century, and the published 
accounts of their travels contain maps of vacancy traversed by 
thin red lines, the results of these route surveys. These travellers 
opened up the country, and they made determinations of the 
latitudes and longitudes of a great number of places, which got 
on to the maps, but which necessarily were often wrong. A great 
deal of trouble has been caused by these errors, owing to the 
ignorance on the part of diplomatists and officials generally of 
the unavoidable roughness of preliminary maps not based upon 
regular survey. It is essential that the sources of information 
should be stated on the margin of all maps pretending to show 
detail. 

The astronomical observations. 

These differ very little in kind from those used in much 
more elaborate work, and we may defer a detailed consideration 
of them, confining ourselves for the moment to an examination 
of the general principles, which are common to voyages on sea 
and on land. 

Latitude^ the distance north or south of the equator, is found by the 
observation of the altitude of a heavenly body as it crosses the meridian.: the 
Sun about noon, or stars at their meridian passages during the night. 

Longitude, the angle between the meridian of the observer and the 
standard meridian, generally that of Greenwich, is measured by the difference 
of times of the two meridians. The local time is determined by observation 
of a heavenly body as nearly due east or west as possible : the Sun in the 
early morning or late afternoon, or stars at the appropriate time of night. 
The Greenwich time is carried by chronometer or watch. (For simplicity 
we exclude for the moment the alternatives of finding the Greenwich time by 
observation, or of receiving it by telegraph cable or wireless.) 

Azimuth, or true bearing, required for the correction of the compass, is 
determined with the local time. 

At sea the ordinary mariner works almost entirely by the 
Sun, and the observation which is familiar to all passengers is 
the noon altitude of the Sun, which gives the latitude. It is a 
very common mistake to suppose that this observation gives the 
instant of noon. This is not so ; the observation which gives 
local time is made somewhat early in the morning or late in 
the afternoon. Thus latitude and longitude are determined at 



ROUTE TRAVERSING 6i 

different times. But meanwhile the ship is under way, and it is 
necessary to have some method of carrying forward the morning 
longitude to the latitude at noon, or of carrying forward the 
noon latitude to the afternoon longitude. This is done by 
keeping the "dead reckoning" of the ship's course. A continuous 
record of the course and of the speed of the vessel on that course 
is kept in the log (the journal of the voyage, not the instrument 
of the same name by which the speed is measured). The dead 
reckoning enables the navigator to make the required allowance 
for the run of the ship between the successive observations, and 
to carry on during cloudy weather. 

The traveller on land works in very much the same way. 
There are obvious reasons why it may be necessary to avoid as 
far as possible observation of the stars by night : mosquitoes 
and the risk of fever are sufficient. In the ordinary course of 
things he will rely largely on observations of the Sun, though 
star work is more accurate. But the requisite observations of 
the Sun must be made, as we have seen, at widely different 
times of day, and the traveller cannot as a rule afford to wait for 
a great part of a day at every place whose position he wishes to 
fix. He is therefore compelled by the nature of the case to use 
some means of keeping account of what the sailor calls his "dead 
reckoning," that is to say, of keeping a current account of his 
position, carried on from one place to another by observation of 
the course he is steering and the rate at which he is travelling. 
He makes, in fact, what is called on land a " compass traverse." 

In modern practice the navigator does not confine himself to 
the old routine of the noon altitude for latitude and the morning 
or evening sight for time and longitude, but in doubtful weather 
he gets an observation whenever he can. An altitude of sun or 
star, at a known standard time by chronometer, fixes a small 
circle of the sphere on which the observer must be at the moment 
of the observation ; and a portion of the circle sufficient to cover 
the range of possible positions can be laid down as sensibly a 
straight line on the chart. A subsequent observation made on 
a different bearing defines another small circle, which intersects 
the first at the position of the observer. Intelligently used this 



62 ROUTE TRAVERSING 

method is of wide generality, and has the great merit of giving 
its full weight to any observation made at any time, while 
avoiding the often troublesome necessity of stopping to make 
the observations at closely defined instants. It does not appear 
that the method has been employed on land, but it is equally 
applicable there for at any rate the rougher determinations of 
position with a small theodolite or sextant. Within a few 
degrees of the pole the application of the method becomes of 
remarkable simplicity. See, for example, a paper by the author 
in the Geographical Journal, March 1910, 

The compass traverse. 

A traverse is defined as a connected series of straight lines 
on the Earth's surface, of which the lengths and the bearings are 
determined. In a compass traverse the bearings are determined 
with the prismatic compass, which differs from an ordinary 
pocket compass in two principal respects : it is fitted with sights 
which can be directed upon a distant object ; and with a prism 
which brings into view at the same time the scale of degrees 
marked round the edge of the compass card. The bearings are 
invariably reckoned in degrees from 0° right round to 360°, 
from magnetic north through east. The complicated system of 
" points," now becoming obsolete at sea, is never to be used 
on land. 

Selecting the most distant conspicuously recognisable point 
upon the line of march, the traveller observes and records its 
bearing, and proceeds to determine, as accurately as circum- 
stances will allow, the distance he has travelled by the time he 
arrives at it, or the length of the " leg." Accurate measurement 
is of course inconsistent with rapid travel. A short distance 
can be paced, but it is not possible to count paces all day for 
days at a time. The legs of a traverse are therefore generally 
measured by cyclometer or " perambulator," or merely estimated 
by time. 

Distances by cyclometer or perambulator. 

The perambulator consists of a wheel of known circumference, 
frequently ten feet, mounted in a fork with a handle, very 



ROUTE TRAVERSING 63 

much like the common child's toy, and fitted with a counting^ 
mechanism to record the number of turns which the wheel has 
made. If a man can be spared from the caravan to trundle this 
instrument — an easy duty which fills the native carrier with 
pride — it is simple to record the length of each leg of the 
traverse in terms of the number of revolutions ; but it is hard to 
tell how much to deduct for the windings of the path and the 
inequalities of the ground. 

The sledge-meter used by Sir Ernest Shackleton and Captain 
Amundsen on their South Polar journeys was a " perambulator " 
wheel carried out on a light spar behind the sledge. Its 
indications were in general remarkably accurate. 

The ordinary cyclometer registers only eighths or tenths of a 
mile, and is too coarse ; a more refined instrument of the kind 
would sometimes be useful. But it is easy to calibrate any 
bicycle so as to know the value of a revolution of the front 
wheel. 



Distances by time. 

The apparent advantages of the perambulator method of 
measuring distances are in practice much discounted by the 
difficulty of knowing what allowances to make for the windings 
of the path. An experienced traveller will obtain results which 
are pretty well as good, without being obliged to spare a man 
for the work, by the simple process of timing each leg of the 
traverse, and estimating the rate of march. The average rate of 
a party on fairly level and unobstructed ground is found to vary 
very little. Practice will enable the traveller to make allowance 
for change of rate over rough or hilly country. The most 
common error is a persistent over estimation or under estimation 
of the rate; and we shall see later how it is possible to keep 
a check on systematic errors of this kind. The most serious 
difficulty is common to all methods of route traverse — that of 
keeping the average direction and estimating how fast one is 
really covering the ground, when marching along a winding 
track through thick bush. 



64 ROUTE TRAVERSING 

Details on the flanks. 

If the country through which the traveller is marching is 
fairly clear he can fix roughly the positions of its principal 
features as he goes along by the method of cross bearings. 
The compass bearings of prominent peaks and other easily 
recognisable objects are taken from different points, and the 
intersections of these lines of bearing, when plotted at the end 
of the march, give positions of the objects in question with a 
degree of accuracy comparable with the general accuracy of the 
traverse. 

At the same time the bearings of all cross tracks and streams 
are taken at the points where they meet the line of march ; the 
character of the ground is recorded at intervals, with any other 
information which can be obtained readily. 

Check by cross bearings. 

A similar process can be used for the opposite purpose, of 
checking the accuracy of the traverse by bearings of a distant 
object whose position is known. For example, in traversing 
round about Ruwenzori occasional bearings of the peak will 
serve as a check on the traverse, and lay down its position on 
the ground. A like method is much used at sea for fixing the 
position of the ship when a known object is in sight, such as the 
Peak of Teneriffe, visible sometimes at a distance of lOO miles. 

The field book. 

The method of recording a traverse is best shown by a page 
of the field book, which is kept by well recognised rules. 

The essential is that it begins at the bottom of what would 
ordinarily be the last page of the book, and goes upwards and 
backwards to the beginning. The columns up the centre contain 
the time of each observation, the bearing of each leg, and the 
estimated rate of progress on that leg, or the number of turns 
made by the perambulator wheel. Detail to the right or left 
flank is recorded in the right or left margin, and it is important 
to note that the page becomes a kind of diagrammatic repre- 
sentation of the country traversed, of which the central columns 
represent a line, the line of march. Hence if a straight stream 



ROUTE TRAVERSING 



65 



or track crosses the route obliquely, the portions represented on 
each flank must not be drawn as parts of one straight line, but 
in the manner shown in the example below. A similar con- 
vention will be found later in the methods of keeping field 
books for other kinds of survey. 



Peak A 127° 




Halt at Z. 

Shade trees and 

good water 



Snow peak A 146° 



Village W 



I I.I4 




3 


10.52 


198 


2| 


10.41 






10.34 


220 


3 


10.7 


234 




8.52 




3 


8.40 


202 


2* 


8.22 


2ig 


2| 


8.5 


223 


2f 


7-57 


246 


3 


7.46 


214 






Leave Camp at Village X 

Time Compass Rate 
Bearing m.p.h. 

Specimen field book. 



Shallow stream 
10 ft. wide 



Track to Y 308° 



Cultivation 



The compass. 

For instrumental details as to the care and use of the 
compass, see page 102. We shall deal here with the particular 
points which are special to compass traversing. 

It is usually essential that the march of the party shall 
not be interrupted while the observations are made, and it is 
generally undesirable that the observer should have to run in 
order to catch up with the party after the observation. If he is 
on foot he will try to walk on ahead to the point of observation ; 
if he is mounted he can afford to spend more time, perhaps 
to dismount and set up the compass on a tripod, which much 

H. M. S. 5 



66 



ROUTE TRAVERSING 



improves the accuracy of the observation. It is clearly impos- 
sible to prescribe any exact rule or programme. Two points 
are to be remembered : the rate of march which is recorded is 
that of the main party, which keeps on steadily, and it is there- 
fore unnecessary for the observer to take account in his time 
records of the short intervals during which he himself is halted 
to make the observations. And secondly, the whole operation 
is a rough and ready affair ; he must therefore be careful not to 




Mag. North 

A 



Fig. 4. Plot of compass traverse. 

waste time in trying to record minute details which have no real 
importance ; small deviations of the track will be ignored so 
long as the general direction is preserved, and it is not necessary 
to take a careful bearing of a cross track which disappears round 
a corner in a few yards. 

In thick bush, where the direction of the path changes every 
few yards, or on the march in a hostile country, when it is 



ROUTE TRA VERSING 67 

impossible to leave the column of march even for a moment, it 
is possible to do a good deal simply by watching the average 
position of the compass card as it is held in the hand while 
inarching, and recording the bearing every five minutes. 

The check by astrononiical observations. 

Even under the most favourable circumstances the error in 
the recorded length of a route traverse will often be ten per cent. ; 
and in a country where the rocks are magnetic, and the compass 
consequently unreliable, the bearings may be affected by large 
errors. It is therefore very important to lose no opportunity of 
checking the traverse by astronomical methods. Particularly 
on long journeys, extending over months, it would be folly to 
rely on the compass traverse only, just as it is dangerous to rely 
for many days on the dead reckoning at sea. 

We may sum up the possibilities of astronomical determina- 
tion as follows : 

Latitude. Observation of latitude, either by the Sun or the 
stars, is easy, and there is no difficulty at all in getting latitude 
within a mile by sextant, or within a small fraction of a mile by 
micrometer theodolite. 

Longitude. Observations to find local time are easy, though 
the calculations are a little long. But the longitude is the 
difference between local time and Greenwich time, and the 
practical impossibility of getting longitudes right within a 
number of miles while upon the march is due to the dif^culty 
■of carrying or obtaining Greenwich time. To carry Greenwich 
time means to carry such a number of chronometers, or better, 
of half chronometer watches, that the mean of their indications, 
corrected for their rates so far as known, is right within a small 
number of seconds. A difference of four seconds of time is 
equivalent at the Equator to a difference of one geographical 
mile. 

The cost of the chronometers, the anxiety of their care and 
transport, and the little reliance that can be placed upon their 
rates when they are exposed to jolting and great changes of 
temperature, make their employment practically impossible. 

5—2 



68 ■ ROUTE TRAVERSING 

Watches carried carefully in the pocket are a little more satis- 
factory, but cannot be trusted absolutely for long. 

Greenwich time. Occultations. 

To find Greenwich time by observation on some other 
meridian, as distinct from carrying it with one, requires the 
observation of the occultations of stars by the Moon, This 
involves, firstly, half an hour's drawing and computation, to 
predict approximately the circumstances of the occultation at 
the place ; for without such a prediction it is impossible to make 
the observations successfully, or even to know whether there 
will be anything to observe. Secondly, there is the observation 
of the phenomenon with a fairly large telescope, of say three 
inches aperture and three feet long — a telescope which is rather 
large and cumbrous to carry. Third, if the observation is 
successful, there is a long computation afterwards, to deduce 
rigorously the Greenwich mean time of the occurrence. And 
finally, a comparison between the calculated time and the time 
recorded by the chronometer at the moment of the occultation, 
gives the quantity we seek, the error of the chronometer on 
Greenwich mean time. It will be believed readily that the 
comparative infrequence of occultations observable, the labour 
involved in the prediction and observation, and the length of 
the subsequent calculations, make this method of limited use to 
the traveller. 

Under special circumstances, however, the method of occul- 
tations may still prove of value. Whenever a skilled and 
enthusiastic observer finds himself compelled to spend a con- 
siderable time in a place of which the longitude is badly known 
he will find it worth his while to predict and observe some 
occultations. Such cases might be, for example, the stay of 
a scientific expedition on an island ; or a polar expedition in 
winter quarters ; or a missionary or consul at some out of the 
way station in China. But wherever the telegraph or wireless is 
within reach the method of occultations is superseded. 

Lunar distances. 

An alternative method of finding Greenwich mean time is by 
the observation of lunar distances, in the way which used to be 



ROUTE TRAVERSING 69 

practised at sea before the vibration of fast steamships made 
accurate observation impossible. This method requires a sextant, 
whereas for every other observation the traveller will do better 
with a small theodolite ; it can be practised whenever the Moon 
is visible with a bright star or planet, and to that extent is 
superior to the method of occultations ; but the results are less 
accurate, and the calculations are long and troublesome. 

We may conclude that the determination of longitude by 
astronomical observation is possible only to those travellers who 
are so fortunate as to have plenty of technical skill, plenty of 
time on the march, and unusual freedom from the ordinary 
anxieties of an expedition. Those who are not so happily 
situated can scarcely hope to keep their longitudes within a 
number of miles. 

Azimuth. 

The azimuth or true bearing of a ray, the angle between the 
ray and the meridian through the line of sight, is different from 
the compass bearing of the ray by the amount of the deviation 
of the compass. Were this deviation constant it would have 
the effect of slewing all compass work round in azimuth, but not 
of altering its shape. But the deviation of the compass varies 
not only from place to place, but also to some extent from 
month to month at the same place. Hence all compass work is 
■incomplete unless it is accompanied by determinations of the 
compass deviation. Such observations consist in finding from 
the Sun or the stars the true azimuth of a given ray, and com- 
paring it with the compass azimuth. 

The determination of true azimuth is made in much the 
same way, and under the same circumstances, as the observation 
for local time, and if necessary can be combined with it. It is 
not a very laborious process, and should therefore be practised 
frequently. 

At sea the observation for the deviation of the compass is 
more frequent than any other observation ; on a well run ship 
an observation is taken every watch, if the weather allows, for 
an unknown error of even a quarter of a degree is by no means 
negligible in the day's course of a fast steamship.' 



70 



ROUTE TRAVERSING 



On land, where the rate of progress is much slower, and the 
compass used is smaller and less accurate, such very frequent 
control is not necessary. But it is essential to control the 
general accuracy of a compass traverse by taking a true azimuth 
from time to time, and an example will illustrate the whole 
process. 

Before starting in the morning the traveller may be informed 
by his guides that the day's march will take him near a distant 
well-marked point. He sets up his theodolite, sets it on the 
distant point, and reads the horizontal circle. Then he turns 
to the Sun and obtains simultaneous readings of the horizontal 




Fig. 5. Observation of Azimuth. 



circle and the Sun's altitude. From the altitude, and an approxi- 
mate knowledge of the latitude, the true azimuth of the Sun can 
be calculated. Apply to this the angle between the Sun and 
the distant point, as measured on the horizontal circle, and the 
azimuth of the distant point is found. Compare this with the 
compass bearing of the point, and the deviation of the compass 
is known. 

Now when at the end of the day's march the route is plotted, 

and the position of the object observed to in the morning has 

been laid down with reference to the route by cross bearings 

aken from ne^ at hand, the azimuth of this object from the 



ROUTE TRAVERSING 71 

starting point, as shown on the drawing, may be compared with 
its true azimuth as found from the morning observation. This 
will provide an excellent check on the general accuracy in 
azimuth of the whole day's traverse. It must not be forgotten 
that, except near the equator, the " convergence of the meridians " 
must be taken into account in plotting a long traverse, but the 
discussion of this refinement may be postponed. 

Check on the length of the traverse. 

We have seen that latitudes may be found very easily to 
within a fraction of a minute of arc, that is, of a geographical 
mile. A comparison between the latitudes taken at each end, 
and the distance made north or south, as shown by the traverse, 
will give an admirable check on the scale of the traverse in this 
direction. 

But it should be noted carefully that before proceeding to 
resolve the traverse into its north-south or east-west components, 
all the bearings must be reduced from magnetic to true bearing. 
The resolved parts of each leg of the traverse may then be 
calculated directly, or they may be taken out from Traverse 
Tables, or from the tables which are called, in the curious 
terminology of the navigator, " Latitude and Departure Tables." 

A similar check on the scale east and west cannot be 
obtained by observations for longitude, for the reasons given 
above ; or at least, it is beyond the reach of the ordinary 
traveller. But if care is taken to check by differences of latitude 
whenever the route leads considerably north or south, there will 
be an excellent indirect control upon the lengths of the traverses 
running east and west. 

Dead reckoning. 

The observation for time or azimuth, morning or evening, 
requires a knowledge of the latitude, which is found from the 
Sun only near noon ; while the observation for latitude requires 
a knowledge of the local time, except in rough sextant work, 
and of the approximate Greenwich time, which cannot be found 
near noon by any practicable field methods. Suppose the 
traveller has obtained an observation for time before setting out 



72 ROUTE TRAVERSING 

in the morning. By noon he will probably have moved into 
a different longitude, and his local time will have changed. 
But his route traverse will give him very nearly the change of 
longitude, and so he can apply the necessary correction to the 
error of his watch which he found in the morning, and thus he 
can obtain his true local time near noon. In the same way, he 
can bring forward the noon latitude to give him the approximate 
latitude required for the time or azimuth observation morning 
or evening. 

It will be seen that this process of carrying forward the 
change of latitude or longitude between one observation and 
the next is very like the process practised continually at sea, of 
carrying on by dead reckoning. 

The details of these astronomical processes need not be 
studied at the present stage. But it seems to be essential that 
the student should have a general idea of the nature of the 
control which field astronomy can exercise over traverses plotted 
by the compass, such as the pioneer traveller makes in his first 
journey through an unmapped country. 

Thus, for example, in the Geographical Journal for January 
19 1 3, among the notes on new maps we find an account of 
a map of a part of the Sahara, published by the French 
Ministere des Colonies, 19 12, "constructed from the itineraries 
and sketches of Captain Cortier, officers attached to his expedi- 
tion, and others It has been adjusted to 33 astronomical 

positions determined by Captain Cortier, a useful table of which 
is given in the lower right hand corner of the map." 

Route traverses cannot make a map. 

A route traverse carefully made is admirably adapted to 
illustrate the account of a journey, and to enable future travellers 
to follow the same route. But it is altogether wrong to suppose 
that anything in the nature of a satisfactory map can be made 
by combining a number of these traverses. Each individual 
traverse will serve very well by itself, until it comes to be fitted 
to other traverses. Then it is invariably found that the separate 



ROUTE TRA VERSING 73 

traverses will not fit accurately together. The reason for this is 
easily seen. Each traverse is a zigzag line, which may have 
been stretched by error in estimating distances, and distorted 
by errors in the mean bearings of tortuous tracks. A certain 
number of points will have been tied down, so far as displace- 
ments north and south are concerned, by the astronomical 
latitudes, and the general bearings of considerable lengths will 
have been controlled by the astronomical azimuths. But within 
these constraints there will always have been plenty of room for 
errors to accumulate. 

Moreover, a number of traverses run across a country leave 
large areas unvisited, and a map cannot be considered worthy 
of the name which shows detail in one part, and leaves out more 
important detail of the same kind in another. Thus the com- 
pilation of traverses cannot make a map. 

The impossibility of making a map by compiling traverses 
is one example of a general principle which underlies the whole 
of Survey : a map must be constructed on a rigid framework. 
And how can such a framework be obtained ? The answer is 
the same in all branches of surveying. By building it up of 
triangles in which the angles are measured, not the lengths of 
the sides. 

It must be understood, however, that when we speak of the 
impossibility of making a map by the compilation of route 
traverses, we mean that a final and accurate map cannot be 
made by .such means. A study of the maps of Africa issued by 
the Geographical Section of the General Staff will show that 
many of these are compiled from such material ; but such 
sheets always bear the legend "None of this country has been 
surveyed"; the compilation is provisional, a little better than 
nothing at all, and as soon as possible it is superseded by 
a regular survey. 

We must make the reservation also that there are cases in 
which the final work of survey must be done by traversing : in 
dense forest regions, and in cities. But this is precise traverse, 
of an altogether different order of accuracy, which will be dealt 
with briefly in Chapter VI, page 162. 



74 ROUTE TRAVERSING 

Heights by Aneroid Barometer. 

The clinometer is good for determining relative differences 
of height over a small range of ground, but is useless for 
carrying forward such determinations over a long distance : the 
accumulation of error would be soon intolerable. The traveller 
therefore requires some instrument to give him rough determi- 
nations of absolute height at a point, and to measure considerable 
differences of elevation under such circumstances as the ascent 
of a mountain peak, where the clinometer is quite inapplicable. 

The pressure of the atmosphere varies with the height above 
sea, and the reading of the barometer varies accordingly. 
Roughly, the barometer falls one inch for each thousand feet of 
ascent. But the pressure of the air and the height of the barometer 
are affected also by the disturbances moving in the atmosphere 
which affect the character of the weather ; and they are also 
dependent upon the temperature of the air. Hence the reading 
of the barometer at any moment is dependent upon a compli- 
cation of circumstances, and can give no precise determination 
of height above sea. One may say, however, that the barometer 
at sea level is rarely above 31 inches, and rarely below 29; so 
that if it is observed to stand at 24 inches, the presumption is 
that the observer is somewhere between 5000 and 7000 feet 
above sea. 

To obtain a clear understanding of the way in which the 
barometer can be used to obtain more precision than this, 
consider the case of a recording barometer carried by train from 
Lancaster to Carlisle. At Lancaster it will draw a trace showing 
the variations in the pressure of the air associated with the 
passage of disturbances or the establishment of anti-cyclones. 
Between Lancaster and Carlisle the train climbs nearly 1000 feet 
over Shap Fell ; the barometer will fall about an inch on the 
ascent, and will rise again as the train runs down the steep 
descent through Penrith. At rest at Carlisle the barometer will 
draw still a variable trace, depending again upon the passage of 
disturbances in the atmosphere. The question is therefore, how 
to disentangle the variations due to height from those due to 
weather, including changes of temperature. 



Plate XI 




I. Aneroid Barometer. 




2. Boiling Point Apparatus or Hypsometer. 



Determinaiion of Heights. 



ROUTE TRAVERSING 75 

It is not safe to assume that the sea level pressure is the 
same at two places fifty miles apart. Therefore if one wishes 
to disentangle the weather changes from the altitude changes, 
it is almost necessary to have a barometer stationary in altitude, 
as nearly as possible below the barometer which is being carried 
uphill. The weather changes of pressure are given by the 
former and applied to the latter ; what is left of change may 
be ascribed to the variation in height of the travelling baro- 
meter. 

In many cases it is not possible to leave a barometer at the 
base camp, to be read while the travelling barometer is away. 
One must then do the best possible by returning to the base 
camp as soon as possible after the ascent, and determining the 
change in the reading there which has taken place during the 
day. Thus, suppose that a climber reads his barometer at 4 a.m. 
before setting out, and records frequent readings during the 
ascent and descent. He reaches the top at noon, and is back 
in camp at 5 p.m. Comparison of the morning and evening 
records at the camp shows that the barometer has fallen half an 
inch during the time the expedition was away, and to compare 
with the noon reading at the summit one must interpolate 
between the morning and the evening readings below. If the 
barometer has been falling regularly throughout the day, this 
will give the correct noon reading at the lower station ; but 
otherwise not ; and the advantages of having a second observer 
remaining below are sufficiently clear. 

Barometer heights in exploratory survey. 

We have seen that accurate results can be obtained only 
when the barometer is used to obtain differences of height 
between two stations which are occupied as nearly as possible 
simultaneously. In general this is not practicable for an ex- 
plorer, who has to push on through a country, and cannot retrace 
his steps, or leave another observer behind at a base camp. 
Such a man must do the best he can to obtain information as to 
the average pressure at sea level in the region where he is 
travelling, and must be careful to make allowances for the 
seasonal and daily variations of the pressure, which in tropical 



76 ROUTE TRAVERSING 

countries are often surprisingly regular, and quite worth taking 
into account. 

In the survey of Southern Nigeria, for example, it is found 
that the diurnal changes of the barometer are so regular that it 
is possible to run fairly accurate contours in the thick forest, if 
care is taken to study and apply the corrections for the diurnal 
variation. 

But with all care it is not possible for a traveller single- 
handed to obtain much accuracy with the aneroid barometer, 
and this explains why the heights of mountains and lakes in 
Africa are often found to be several hundred feet wrong, when 
the early barometer heights are at last compared with the results 
of precise surveys. 

Instrumental precautions. 

The aneroid is a delicate instrument, and must be treated 
with all care. It must be allowed some minutes to come to rest 
before a reading is taken after a rapid change of altitude ; the 
process is hastened by gently drumming with the fingers on 
the case of the instrument ; but hard tapping is bad for the 
instrument, and all shocks must be avoided. 

An ordinary aneroid carried for a long time at a great 
height, say over nine thousand feet, is liable to become strained, 
and its readings inaccurate. Special types of instrument, called 
Mountain Aneroids, are made for use at great heights. But if 
it is necessary to use an instrument of the ordinary pattern, 
a simple device will preserve it in good order. A well-fitting 
tin has a bicycle valve soldered into it. The aneroid is placed 
inside, the joint sealed with surgeon's rubber paster, and the tin 
is pumped up with a bicycle pump until the pressure inside is 
near the normal sea level pressure. The aneroid will travel thus 
without strain, and can be taken out when required. This 
arrangement was found to work very well by a traveller in the 
Andes. 

Temperature corrections. 

The aneroid barometer is corrected for the effects of 
temperature upon the instrument itself; but it is necessary to 



ROUTE TRA VERSING 77 

take into account the temperature of the intervening air between 
the upper and the lower stations. This cannot be done accu- 
rately, and the method suffers in consequence. It is seldom 
possible to do more than to take the mean of the temperatures 
at the upper and the lower stations, and to treat this as the 
mean temperature of the intervening column of air. When 
there is no lower station for comparison, and some assumption 
has to be made as to the temperature below, the results become 
still more uncertain. 

Heights by Barometer. 

There are two sets of tables in common use, those calculated respectively 
by Loomis and by Baily. Both are given in Atixiliary Tables of the 
Survey of India ; the former are given in Hmts to Travellers, published 
by the Royal Geographical Society ; and the latter in Textbook of Topo- 
graphical Surveying (Close). 

In none of these places is there an adequate account of the basis of 
construction of the tables, and it does not appear that any such account 
is readily available. A brief summary is therefore given here. 

An investigation of the theory of the subject is to be found in Laplace, 
Mdcanique Celeste, Vol. iv, p. 289 of the edition of 1805. With some 
modifications, this leads to the following" formula": 

If H =height of barometer at lower station, 
H'= „ „ „ „ upper „ 

T = temperature of barometer at lower station, 
T'= „ „ „ „ upper „ 

/ = ,, „ air at lower station, 

t' = „ „ „ „ upper „ 

X =the latitude, 

.y = height of lower station above sea level, 
X = difference of height of two stations, 
/x = modulus of common system of logarithms, 
6 = difference of expansion between mercury and the metal of which 

the barometer scale is made, 
a = radius of the Earth. 

Then x = Px{\ogII-\og N' - ,xd{T- T')} 

( t + t'- 64] . , 
X -^ I H y [when temperatures are on the 

Fahrenheit scale] 
X {i + o'oo265 cos 2A} 

[ a J 



X 1 + 



78 ROUTE TRA VERSING 

Taking heights in feet, the constant P is 60159, according to Loomis ; 
<? = 20"89X 10'' feet, and the constant multipHed by 116 is 2'34i. 

Hence 

;i-={6oi59 (log //- log i¥')- 2-341 (r- r)} 

to allow for the mean temperature of the air 

900 / '' 

and an average amount of aqueous vapour 

x(i 4-o'oo265 cos 2X) to allow for the variation of gravity with 

the latitude 

I + ' ^-TT^ ^ ) to allow for the diminution of gravity 

20-89 X lo*" y b 1 

with height. 

Loomis' Table I gives the values of 60159 log//- 27541 for values oi H 
from II to 31 inches. He gives no explanation of the reason for the choice 
of this constant 27541, and its significance is not obvious. He remarks 
merely that it does not change the difference of the two quantities taken 
from the table. 

We enter Table I with the two quantities H and H\ and take their 
difference. This gives a first approximation to ,r, the difference of height 
between the two stations. 

Table II gives the values of 2-341 {T— T'). It should be noted that this 
correction is required only when mercurial barometers are used, which is 
seldom. Aneroid barometers are mechanically compensated for their tem- 
perature, and no correction is then required on this account. 

The resulting difference of height is then multiplied by the factor 

, /+/'-64^ 

i-j 

900 

no table being provided for this process. The result is a close approxima- 
tion to the final result. 

Table III gives the value of .rx 0-00265 cos 2X, by a table of double entry 
with arguments x and X. 

The correction for the variation of gravity with the height is split into 
two parts. 

Table IV gives the correction equivalent to multiplication by the factor 

I A J>-'-'^ .- ■ the part involving the difference of heights. This is a table 

20-89 X 10" f » 

of single entry with argument x. 

Table V gives the correction equivalent to the remainder of the factor 

— . But since s is not necessarily known, though to the approximation 
a 

required it may be deduced from the barometer reading at the lower station, 

* 52251 = 60159 X 21X. 



ROUTE TRAVERSING 79 

the correction is arranged in a table of double entry with arguments H 
and X. It may be noted that this table is unnecessarily extended. If x, 
the difference of heights, is 25000 feet, the barometer at the lower station 
can hardly be so low as 16 inches, corresponding to an elevation of about 
16000 feet. 

The above is the form of the tables as given by Loomis, and reproduced 
without comment in English books up to the present day. But it should be 
remarked that they are slightly erroneous in Table IV. The factor 

;r+;22;i 



is required in the reduction of observations made with mercurial barometers. 
But the aneroid is equivalent to a spring balance, which in itself is inde- 
pendent of variations in the intensity of gravity. A reference to the theory 
shows that when aneroid barometers are used, the term 52251 should be 
omitted ; and this is the greater part of the correction tabulated in Table IV. 
We shall avoid this error if we omit altogether the correction from Table IV; 
and enter Table V with the mean of the barometer heights at the two stations, 
instead of with the barometer height at the lower station. 

We may note also that as Loomis' tables are commonly printed, the 
argument at the side of Tables IV and V in the column headed "height" 
is misleading. The column should be headed " difference of height of the 
two stations." The examples given in Hints to Travellers are wrong in 
this respect. The height of the upper station has been entered, instead of 
the difference of heights. 

The tables in the form given by Baily are a modification of the above. 
Baily takes as an average case that s, the height of the lower station, is 
4000 feet, and that x, the difference in height of the two stations, is about 
3000 feet (though he does not say so in the latter case). With these as- 
sumptions, the tables are shortened ; but they are arranged so that the 
computation must be done by logarithms, which is less convenient for 
the traveller. It does not appear, then, that the form given by Baily 
has any advantage over the form given by Loomis ; and the results are 
not quite so accurate in theory, because of the assumptions indicated 
above. 

Both Loomis and Baily neglect the variation in the amount of moisture 
in the air, and are content to arrange their constants to correspond to an 
average amount of moisture. The recent tables by M. Angot, as now 
published in the Anmiaire dii Bureau des LoJigittides, give means of 
allowing directly for the moisture of the air, and are in this respect a 
great improvement on the older tables. 

But it may very well be doubted if it is of much avail to take account 
of refinements such as the variations of gravity with height and latitude, 
and variations of the aqueous vapour present in the air, while the crude, 
though inevitable, assumption is made that the average temperature of the 



8o 



ROUTE TRAVERSING 



column of air between the two stations is the mean of the temperatures at 
those stations. This cannot be exact ; and it will be seen that the error 
introduced by this assumption may very well be much greater than the small 
corrections due to the other causes. 

The tables for the calculation of Barometer heights. 

The following brief table i.s not sufficiently extended to be 
convenient in the actual calculation of observations. It is given 
here only that we may have an example of the style of the 
principal table, and of the magnitude of the quantities involved. 
For the reasons given above, we have not thought it necessary 
to give any table of the small corrections whose effect is trifling 
compared with the uncertainty of the principal temperature 
correction. 



Bar. 




Diff. 


Bar. 




Diff. 


in 


Feet 


for 


in 


Feet 


for 


inches 




o'l inch 


inches 




01 inch 


I2-0 


3670 


217 


22'0 


19506 


119 


13-0 


5761 


201 


23-0 


20668 


114 


i4'o 


7698 


187 


24-0 


21780 


109 


15-0 


9500 


174 


25-0 


22846 


104 


i6'o 


1 1 186 


164 


26-0 


23871 


100 


17-0 


12770 


^54 


27-0 


24857 


97 


i8-o 


14264 


145 


28-0 


25807 


93 


i9"o 


15676 


137 


29-0 


26724 


90 


20-0 


17016 


130 


30 'O 


27610 


87 


210 


18291 


124 


31-0 


28466 


84 



Take the difference of the heights corresponding in the above table to 
the barometer at the upper and lower stations. 

To correct for temperature, multiply this difference by 

yjjj (sum of air temperatures at the two stations — 64°). 

The boiling point thermometer. 

The pressure of the air affects the temperature at which 
water boils, and a determination of the boiling point of water 
thus affords an independent determination of the pressure of 
the atmosphere, and gives the same kind of limited information 
as to height above sea as is given by the aneroid barometer. 
Since it is not possible in the field to carry thermometers which 
can be read to less than one-tenth of a degree Fahrenheit, and 



ROUTE TRAVERSING 8i 

one-tenth of a degree in the boiling point corresponds to a 
difiference of pressure which is in its turn equivalent to a dif- 
ference in height of about fifty feet, it follows that the boiling 
point thermometer is less sensitive than the aneroid for deter- 
mining differences of height. But on the other hand, it is less 
likely to become deranged, and it is therefore well to carry both 
instruments on a journey, and to use the boiling point apparatus 
to control the general accuracy of the barometer. 

The following is an abbreviation of the usual table for the relation 
between the boiling point, the barometer, and the difference of height 
between stations. 







Height in feet above the 


Boiling Point 


Equivalent Barometer 


point at which water 
.boils at 212° 


212° Fahr. 


29-921 





2IO 


28746 


1046 


208 


27-613 


2097 


206 


26-521 


3151 


204 


•25-466 


4210 


202 


24-447 


5278 


200 


23-461 


6354 


198 


22-507 


7439 


196 


21-584 


8533 


194 


20-690 


9638 


192 


19-828 


10750 


190 


18-998 


1 1867 


188 


18-199 


12988 


186 


17-426 


14124 


184 


16-681 


15266 


182 


15-964 


16412 


180 


15-275 


17567 


178 


14-611 


18725 


176 


13-970 


19897 



A second table is usually added, giving the factor by which the above 
differences should be multiplied to allow for the mean temperature of the 
intervening air. This is based on the assumption that the temperature at 
the upper station only is observed, and that the mean temperature may be 
derived from the approximate law that it decreases 1° F. for every 330 feet 
of ascent. 

It appears that when the temperature at the lower station is observed, 
or can be estimated approximately, it is better to correct for temperature 
as in the calculation of barometer heights. 

H. M. s. 6 



82 ROUTE TRAVERSING 

In a collection of survey tables it is usual to find the tables 
for the reduction of boiling point observations -given in the 
above form; and no allowance is made for the small corrections 
due to change of gravity in different latitudes, or for different 
altitudes of the lower station. These are small compared with 
the uncertainties of the thermometer reading. But it is well to 
note that the most correct way of reducing the observations is 
to translate the boiling points to the corresponding barometer 
heights, by tables such as that given above, only more extended ; 
and to complete the calculation as for aneroid readings. 

Instrumental precautions. 

The principal point to attend to is that the bulb of the 
thermometer must not be allowed to dip into the water which 
is being boiled, because any impurity present in the water 
alters the temperature at which it boils. The bulb should be 
suspended so that it is fully exposed to the steam which is 
coming off, but is just clear of the liquid itself With this 
precaution it is possible to make the determination of boiling 
point a part of the ordinary cooking operations, as was done 
on the recent British Antarctic expeditions. The thermometers 
were inserted through the lid of the cooking pot and were read 
at each halt. This check upon the barometers was particularly 
valuable under the circumstances, because there was good reason 
to doubt the unconfirmed results of aneroid barometers working 
at elevations of over 10,000 feet, in intense cold. 

It is of course essential that the errors of the thermometers 
employed should be verified at the National Physical Laboratory 
before the start of the expedition, and again on its return. The 
thermometer tends to lower its zero point for a long time after 
manufacture, at a gradually decreasing rate. Old thermometers, 
well standardised, are therefore more trustworthy than new ones. 



CHAPTER IV 

SIMPLE LAND SURVEY 

The settler's land survey. 

As soon as a country becomes settled townships are projected, 
mining areas are pegged out in claims, and the land is parcelled 
out into farms. These operations are usually simultaneous with, 
if they do not actually precede, the establishment of a settled 
government. Thus, for example, we read in the Colonial Survey 
Report, No. i, page 23 : East Africa Protectorate, 1903, "Since 
no survey existed, and it was imperatively necessary to settle 
the people on the land advertised as open for selection, every 
kind of makeshift had to be adopted to meet the situation. 
Much wasteful expenditure was incurred, and the settlers had 
legitimate grievances against the Government." On the average 
a settler was kept waiting I2"6 months for allotment. 

The need of a map of the country is felt acutely from the 
first day of its opening up. But the production of a map is 
a long and costly business, and almost always has to wait. In 
the meanwhile some kind of plan of each township, mine, and 
farm is absolute necessity, both to the occupier and to the local 
administration. Land surveyors set to work to survey the 
properties as they are ready for allotment, or perhaps as they 
have been already occupied, and the result of their labours is 
a series of plans, which accumulate in the office of the Com- 
missioner of Lands. 

We must remember that these are not maps. A topographical 
map shows the natural features of the country, and in addition 
the principal features in the way of communications that have 

6—2 



84 SIMPLE LAND SURVEY 

been added to it by man. But a map does not show the 
boundaries of property, and a map is not on a scale large 
enough to show details and areas sufficient for the purposes 
of property record or of local taxation. The cadastral, or 
property survey, on the other hand, is made on a scale suffi- 
ciently large to show all the details of boundaries, walls, fences, 
and ditches ; and areas of each plot may be measured from it. 
But in general it shows nothing of the relief of the ground. 

A topographical map is in the nature of a picture, a cadastral 
map is a mere diagram of the ground. For reasons which will 
appear in due course it is not possible to construct a map by 
piecing together a set of contiguous property surveys ; and to 
a great extent the work put into the original surveys of property 
is wasted because it has to be done over again when the time 
comes for a regular survey of the country. The sooner that 
comes, the greater the eventual economy. But since it is not in 
practice possible to insist that a regular survey of the country 
should precede any of this detailed property survey, it will be 
convenient to consider here very briefly the principles upon which 
these preliminary land surveys are conducted. It will be under- 
stood that since this book is to deal with maps, and not with 
the minutiae of property and town survey, the treatment of this 
latter can be nothing more than a sketch. 

The elements of property survey. 

Suppose, in the first place, that the plot to be surveyed is 
small in extent, but that there is a great deal of detail in the 
nature of crooked boundaries, buildings, etc., that must be shown. 
The plan will be made by the simple process of land survey with 
chain or tape. 

The principle of land survey is that every detail must be 
fixed by measuring its perpendicular distance from a straight 
line, and the position on that line of the foot of the perpen- 
dicular. Suppose, for simplicity, that a boundary is made up 
of a series of short straight lengths AB, BC, CD, DE, EF, .... 
Suppose a straight line KL is laid out as near as may be to the 
boundary, and that perpendiculars Aa, Bb, Cc, ... are drawn from 
A, B, C, ... to KL. Measure the lengths of the perpendiculars, 



SIMPLE LAND SURVEY 



85 



and the distances Ka, Kb, ... KL. A plan of the boundary 
AB ... E ... may now be drawn as follows: Draw the line KL 
on any desired scale, and lay off the distances Ka, Kb, ... on it. 
Erect perpendiculars from a, b, ... and lay off on them to scale 
the measured distances a A, bB, ... ; we have then transferred to 
the plan the relative positions of A, B, C, ... E. Join them up, 
and we have a plan of the boundary. 

The measurements along the line KL are made with the 
surveyor's chain or with a steel tape; the perpendicular distances, 
called offsets, are measured with a graduated offset rod, if they 
are short, as they should be. 



d 
Fig. 6. 



/ 



When offsets are not short they must be measured with the 
chain or tape ; and it is then necessary to have some such 
instrument as the cross staff or the optical square, to set out the 
offsets perpendicular to the chain line. But long offsets are 
used only in rough work, and it is a cardinal principle of 
accurate land survey that offsets must not be long. A chain 
line must pass near every point that has to be fixed. The first 
thing to attend to, therefore, in making a land survey, is to lay 
out a suitable system of chain lines. 

Suppose, for example, that the plot ABCD is to be surveyed. The 
elementary, often practised, but es- 
sentially bad method, would be to 
chain from A to C, and take offsets 
on each side oi AC to the salient 
points of the boundary. This would 
be a bad, or at least untrustworthy 
method, (i) because the offsets are 
long, and the perpendiculars must 
be laid out with some elaboration ; 
and (2) because there is no check 
upon the result except doing it all 
over again. 

The proper method is to break 
up the ground into triangles. Chain from a \.o b, b to c, and c to a, taking 




S6 SIMPLE LAND SURVEY 

offsets to the boundary along each chain line. The offsets are now short, 

and are easy to measure with sufficient accuracy. Do the same from 

a to d, and from d to c. But 

now note that the construction on ^^--l^-^ 

our plan of the triangles adc, adc, ^^^^^^ "^^^^'^v^ 

depends on the accuracy of the /^ ^^^"^^^^ 

measures of the lengths of our /■ ' ". ^>s^ 

chain lines. An error in one would A^ ^ '^^ 

completely wreck the whole plan. \ '. /y 

Therefore they are to be checked \s '. , / 

1 -IT 1 \ ^ « 1- / 

by measunng the hnes across the \- -/ 

corners kl, 7nn. When the plan \\ ^'/^ 

is drawn out these distances, as \-^ ,y^ 

measured on the plan, must agree ^^dJ^ 

with the actual distances measured n 

in the field. If they fulfil this con- p- g 

dition, then we have a complete 

check on the main structure of the work. If they do not, the fact that 

there is an error somewhere is detected at once. 

It has been mentioned already that a plan does not generally 
show the inequalities of the ground. It is one of the principal 
objects of a map to do so. But whether the inequalities are 
indicated or not, the plan or map must indicate the relative 
positions and distances of all objects as if they are projected by 
vertical lines on to a level surface. Distances must be measured 
and represented as horizontal distances, and the distinction is 
by no means insignificant in the case, for instance, of property 
on the side of a hill. In all land surveying by chain and offset 
rod, therefore, the chain and rod must always be held horizontal; 
and the horizontal equivalent of a distance down a slope will 
be measured in a series of steps. When a slope is steep this 
becomes difficult, and it is evident that the chain lines must 
be chosen so that they are as level as may be. 

In theory land surveying is exceedingly simple, consisting 
only in measuring along the sides of the triangles, and taking 
offsets to all detail. The whole art of it in practice lies in 
selecting the system of chain lines so that they shall form as 
rigid a framework of triangles as can be made. If the three 
sides of the triangle are known with absolute precision the 
triangle can be constructed rigidly, within the limits of accuracy 




SIMPLE LAND SURVEY 87 

of the draughtsman. But errors will creep into the measure- 
ment of sides, and the draughtsman cannot draw with absolute 
accuracy, It is therefore necessary that the triangle shall be 
" well conditioned," as nearly equilateral as may be. 

For consider the construction of a triangle Avith an acute 
angle C opposite the base y^ ^. The 
point C is to be found by describing 
circles with centres A and B, and of 
radii equal to the measured lengths 
AB, AC. These circles will inter- 
sect at an angle equal to C, and 
it is evident that the more acute 
the angle, the greater will be the 
error in the position of C caused l^ig- 9- 

by an error in one of the measured lengths. 

The same kind of argument applies in all branches of 
surveying that depend upon triangulation of any kind : that 
is to say, in all kinds of survey except the simple route traverse. 
There must be no unduly acute angles in the triangle. 

The method of chain survey is well adapted to making plans 
of small detail. The plan of each triangle, and of the points 
fixed to it by offsets, has considerable accuracy in itself But 
it will be understood easily that a large estate cannot be 
surveyed in this way, in a number of small triangles, because 
every triangle is inaccurate to a small degree, and the effects of 
these small errors rapidly accumulate when an attempt is made 
to fit a large number of the triangles together. In this, as in 
all branches of survey, it is impossible to make an accurate 
extensive map or plan by piecing together small portions 
surveyed independently, to build up a large map from small 
blocks. To take the exactly opposite way is the right course. 
Construct a simple framework covering the whole extent of 
land to be surveyed ; get this framework so accurately made 
that it cannot be in error by an amount visible to the eye on 
the scale which is proposed for the map ; and hang the detailed 
survey upon this framework. An accumulation of error is then 
impossible. 



88 SIMPLE LAND SURVEY 

It follows from this principle that a property survey of 
whatever size must begin with a few big triangles covering the 
whole property, and work downwards from these to the smaller 
triangles in which the detail is surveyed. But lines a mile 
long cannot be measured conveniently with a chain, except in 
very flat and open country : some obstruction or other will be 
continually intervening to break the line and make a detour 
necessary. Hence in making the survey for a township, a large 
estate, or a mining concession, we must lay out the principal 
triangles with some more handy and convenient instrument 
than the chain. Such an instrument is the theodolite. 

Our next section will therefore deal with the elements of 
triangulation with a theodolite. 

Simple triangulation with the theodolite. 

Considered in the simplest possible way, the theodolite, as 
used in triangulation, consists of a graduated circle fixed in a hori- 
zontal plane ; a telescope which can be rotated about a vertical 
axis passing through the centre of this circle ; and a pointer 
attached to the telescope, which can be read against the circle. 

We shall postpone to Chapter VIII the consideration of all 
the instrumental details of the theodolite, and for the moment 
confine our attention to the outlines of the method. 

Suppose that we have three points A, B, C marked on the 
ground in some visible way, and that the theodolite is set up 
over A. It is pointed on B, and the 
reading of the pointer on the circle 
is recorded ; it is then pointed on C, 
and the circle is read again. The 
difference between the two circle 
readings will be the angle BAC. 
The theodolite is then moved to B, 
and the angle ABC is measured ; pj ^^ 

then to C, and the angle ACB is 
observed. These three angles should of course add up to i8o°, 
unless the triangle is so large that the curvature of the Earth 
must be taken into account ; and this will be a check upon the 
accuracy of the observations. 




SIMPLE LAND SURVEY 



89 



When the three angles are known the shape of the triangle 
is known, but not its size. To get its size we must measure the 
length of one of its sides ; and then by a very simple piece of 
trigonometry we calculate the lengths of the other sides, from 
the known values of the angles. 

In a triangulation, therefore, we must measure the length of 
one of the sides of one of the triangles. The lengths of all the 
other sides of the whole triangulation will be worked up by cal- 
culation from the observed angles and the length of the initial 
side, which we call the base. 

Suppose, then, that we have selected six points on our ground, A, B, C, 
Z>, E, and /% disposed so as to form the triangles of our figure, of which, it 
will be observed, no one has a very acute angle. Each point must be visible 
from the other points of the triangles to which it belongs ; but it is not at all 
necessary that all the points should be intervisible. For example, C must 
be visible from all five others ; B from A, C, and D ; but E need not be 
visible from A or B. These points are marked by pegs driven into the 
ground, and signals are erected over them. 




The theodolite is set up over each peg in turn, the signal being removed 
if necessary, and the angles in the triangles are measured. Each triangle 
is checked by the necessity that the sum of its angles should dififer from 
180° only by the small quantities which may be allowed as errors of 
observation. 

It is important to notice that, though the points of the triangulation may 
be at different elevations, the angles that are measured are the angles of the 
projection of the figure upon a level surface. For suppose that in the triangle 
ABC the point B is higher than A, and C higher than B. If we wished to 
measure the true angles of the triangle ABC we should have at each station 



90 SIMPLE LAND SURVEY 

to tilt the theodolite so that the graduated circle lay in the plane of the 
triangle. If, on the other hand, we keep the circle horizontal, what we 
actually measure is not the angle BAC, but the angle between the vertical 
planes through AB and AC respectively; which is of course equivalent to 
the angle at A in the triangle ABC projected on the level. But this is 
what we want ; we have already remarked that the plan or map must 
represent the projection upon a level surface, not the actual configuration 
upon the undulating surface of the ground. 

When all the angles are observed we have the shape of the figure. One 
side must be measured, and any one of these will do. We shall naturally 
select the one that lies on the most level and unobstructed ground. We 
suppose it is AB which is measured with chain or tape. Then in the 
triangle ABC, knowing all the angles and one side, we can easily calculate 
the lengths of AC and BC. 

One of the sides of A CD thus becomes known, and the others follow 
immediately, since all the angles are known, as before. 

In this way, from one measured side of one triangle only, we arrive 
at the lengths of all the sides of all the triangles. 

For an example of the calculation, see Chapter VI, page 156. 

Choice of base, and connection with triangulation. 

Having arrived at the principles of triangulation, we must 
now see how they can be put into practice conveniently. 

The stations of the triangulation will naturally be for the 
most part on the summits of hills, from which an extensive 
view can be obtained. But it will generally not be convenient 
to measure from one of these stations to the next, because the 
intervening ground will not be open and level, and otherwise 
suitable for the purpose. In practice, therefore, one chooses a 
site for the base, and arranges a special piece of triangulation to 
connect it with the nearest side of the main system of triangles. 

Suppose AB is the base, and EF the nearest side of the triangulation. 
Select two points C and D, lying on opposite sides of the base, so that the 
triangles ABC, ABD are well shaped or conditioned ; and at the same time 
the triangles CDE, CDF are also well conditioned. Erect beacons at 
A, B, C, D, and, of course, also at the principal triangulation points. For 
the present we shall not examine the method of constructing beacons. For 
this see Chapter VI, page 139. Set up the theodolite successively at the six 
stations, and observe along the rays drawn in the figure. For example, at C 
observe to E, A, D, B, and F. 

Now in the triangle CAB we have all the angles known, and one side 
AB ; hence we can find the length of BC. Similarly in the triangle DAB 



SIMPLE LAND SURVEY 



91 



we find DB from A B. Then in the triangle BCD we know both sides BC, 
BD, and through either of them we find the length of CD. Then working 
through the triangles CED, CFD^ we find CE or CF., and thence from the 
triangle CEF we find EF. 

Our base AB has now been extended through a series of carefully planned 
triangles to EF, which is several times the length of AB., and is one of the 
sides of the principal triangulation. 




It will be noticed that we might have arrived at the length of EF from 
^5 by a number of different ways. For simplicity we have spoken as if 
there were only one way round, but at a later stage we shall see that the other 
ways must not be neglected in accurate work. If, however, we consider 
more than one way round, this difficulty will arise, that since all the 
measured angles are subject to errors of observation, the whole figure is 
slightly inconsistent in its various parts, and we should get slightly different 
results for the length of EF according as we derived it from AB by one 
route or the other. This would be intolerable in practice, and we must 
devise a way of getting over the difficulty before we come to deal with really 
accurate work. In small pieces of isolated survey the question hardly arises. 



The main triangulation. 

Having derived the length of the side EF, a side of one of 
our main triangles, from the measured base AB,v^q can complete 
the triangulation through G, H, K ... until the whole ground 
that we propose to survey has been cut up into a small number 
of relatively large triangles, of which all the angles have been 
observed with the theodolite, and the lengths of all the sides 
deduced from the measured base through EF. 



92 SIMPLE LAND SURVEY 

The next step depends upon the size of our ground. If it is 
not more than say ten miles square we shall make no serious 
error if we neglect the curvature of the Earth, and treat it as 
plane. In that case the triangulation may be laid down upon 
the sheet of the plan simply by constructing the triangles in 
succession from the calculated lengths of their sides ; or more 
accurately by calculating the rectangular co-ordinates of the 
triangulation points with reference to one taken as origin. But 
in order to get the plan orientated we shall want to know the 
true bearing of one side, say EF. This may be obtained very 
roughly with the compass, or very quickly and accurately from 
an azimuth of the Sun. 

If the ground is much larger than ten miles square we may 
not be able to afford to neglect the curvature of the Earth. But 
this case may be reserved for the chapter on Topographical 
Survey. See Chapter VI, page 152. 

The advantages of triangulation. 

Let us look again for a moment at the reasons for making 
this framework of a few big triangles covering the ground which 
we propose to survey in detail afterwards. Suppose that our 
base is only a few hundred feet long, and that the country is so 
rough that we cannot hope to find a place where we can measure 
a longer length on the ground with any accuracy. It is very 
easy, and does not require any special precautions, to measure 
this base with an accuracy of one in ten thousand. If our 
triangles were quite exact we should arrive at the lengths of our 
longest sides with the same proportional accuracy. This will 
not be achieved in practice, but the diminution in accuracy can 
be controlled by the amount of care that we are willing to give 
to the triangulation. Suppose that it is so done that the error 
in the side most remote from the base is increased to an 
uncertainty of one in three thousand. The principal points 
being related to one another with this degree of accuracy it is 
not possible for error to accumulate over any considerable part 
of the plan to a greater extent than this. In cutting up the 
bigger triangles into smaller, either with the theodolite or with 
the chain, local errors may be made, but their effects are not 



SIMPLE LAND SURVEY 93 

cumulative. They cannot extend outside the particular triangle 
in which they are made. 

Again, if only we can find points for the principal triangles 
which are visible from one another, the accuracy with which they 
are fixed is independent of the character of the intervening 
ground, which may be of a kind to render any sort of linear 
measurement impossible. 

Or, to put it another way : It is very hard to measure 
distances accurately with chain or tape except upon open and 
level ground ; it is very easy, by means of the theodolite, to 
measure angles from one well-defined point to another. We 
shall expect, therefore, to do well with a method that gives us 
the triangles by measuring their angles, and requires that one 
side only shall be measured, for which a site can be chosen in the 
most favourable place. 

Town and forest survey. 

There are two cases in which the ordinary method of 
triangulation with the theodolite breaks down: in towns, where 
the walls and buildings make the triangulation impossible ; and 
in dense forest such as the Gold Coast, where the hills are round 
topped and cannot be cleared, and where it is impossible to 
obtain a view of any importance. 

In such cases it is necessary to traverse with the theodolite. 
For this method see Chapter VI, page 162. 

The dangers of patchwork survey. 

We began this chapter with the needs of a survey more 
extensive than could be undertaken by chaining alone, yet only 
an isolated piece of work, such as the plan of a township, 
a mining concession, or an area open to allotment or sale to 
settlers. The principles of triangulation are the same, whether 
the survey is an isolated patch or part of a complete scheme for 
the whole country. But it is important to have a precise idea of 
the dangers and the bad economy of doing survey work in small 
patches instead of making each operation part of a large scheme 
for the complete map. 

In a new territory, where land belongs originally to the 



94 SIMPLE LAND SURVEY 

Government, and is sold piecemeal, the only secure method of 
delimiting the boundaries of property is by reference to a 
complete triangulation of the country. This is forcibly stated 
in a letter addressed by Sir David Gill, then Her Majesty's 
Astronomer at the Cape, to Earl Grey, who in 1897 was 
administering the Government of Rhodesia. The following 
extracts from this letter are taken from the introduction to the 
Report on the Geodetic Survey of South Africa, Volume III. 

" The point which it is always difificult to bring home to the lay 
administrative mind is that it is impossible to survey a country properly or to 
grant indisputable titles to land by surveys made in a patchwork way. 

"When Government has a particular bit of land to be disposed of, it seems 
to be supposed that one has only to send a surveyor to set up beacons, 
survey the ground, and bring back a diagram of those beacons — and sell the 
land according to this description. 

"Assume the surveyor to be competent and honest, the result will be 
certain points marked on a piece of paper, representing pretty accurately the 
shape of the piece of land so surveyed ; but in many places there will be no 
sufficiently well-marked topographical features, such as well-defined river 
boundaries, etc., to locate precisely where in the country the particular farm 
is ; there will be nothing to indicate the latitude and longitude of any 
particular feature of the map (i.e. its position on a general map of the 
country) ; and there will be no accurate topography on the diagram, because 
the price which the surveyor receives for such survey makes it impossible for 
him to include accurate topography in his work. With the approximate 
methods of base measurement necessarily used by such a surveyor there will 
also be some appreciable error in the scale of the map ; and beyond a rough 
orientation by compass (and the direction of the magnetic meridian is subject 
to large secular variation), there is nothing to indicate the true north of 
the diagram. 

"Afterwards, when you come to patch such surveys together, you can see 
that no small trouble must arise, and that shortcomings and overlaps occur.... 
Then comes the further possibility, the dishonest proprietor. A particular 
piece of land is bought from Government. The proprietor finds a 
convenient spring or piece of rich land outside his boundary ; there is no 
neighbour to be hurt, or perhaps only a distant proprietor. It is not a 
difficult matter to shift a beacon — there is no one particularly interested, and 
the beacon is shifted.. ..In this way large tracts of land have been stolen from 
Government in Cape Colony. 

"There is one, and only one remedy for all this, and that is to connect all 
detached surveys with a general system of triangulation ; and it will save 
the Government and the inhabitants generally a vast amount of money to 
establish this triangulation as quickly as possible." 



SIMPLE LAND SURVEY 95 

We are here in the difficulty that embarrasses all Governments 
of new territories : they cannot grant proper titles to the land, 
nor carry on any of the operations of settlement, until the 
country is properly surveyed ; and they cannot afford to have 
the survey made until the country has begun to pay its way, 
and the more urgent demands for roads, bridges, and railways 
have been met. All that can be insisted on is that there must 
not be a month of unavoidable delay in setting to work on the 
complete survey of the country. Every pound that is spent in 
patchwork survey for special purposes is very largely wasted. 

Simple levelling. 

The plan which results from triangulation, either by chain or 
theodolite, represents the ground as if it were all projected upon 
a level plane ; and no attempt has been made, so far as we have 
gone, to show the undulations and inequalities of the surface. 
To do so fully would require the construction of contours, to 
represent the courses of lines running at definite intervals of 
height above sea level. But this belongs rather to topographical 
mapping than to the survey of a small area, and it will be 
treated later. 

Without aiming at a complete system of contours, it will 
usually be necessary to have some knowledge of the variations 
of height above sea, for local purposes of drainage or irrigation ; 
and this at its simplest involves running certain lines of levels 
across the plan, by the use of the surveyor's level and staff 

Putting aside for the time all the details of construction and 
adjustment of the instrument, the level may be described as a 
telescope which is set at right angles to a vertical axis, and can 
be swept round in a horizontal plane. Any object seen on the 
cross wires of the telescope is on the same level with them, or 
with the centre of the object glass of the telescope. 

The levelling staff is a pole, usually rectangular in section, 
with a face divided into feet, tenths, and hundredths of a foot, 
numbered from the bottom upwards. (Plate XII.) 

Suppose that this staff is stood upon the ground at a distance from the 
level, and that the observer, looking through the telescope, sees that the 
horizontal wire cuts the image of the staff at the height 7"6i feet, whereas 



96 



SIMPLE LAND SURVEY 



the centre of the object glass is 4'27 feet above ground. It is clear that the 
ground at the base of the staff is 7"6i — 4'27 = 3'34 feet below the ground on 
which the level stands, provided that the telescope is really pointing 
horizontal. 

Similarly, if the reading of the horizontal wire is 9"03 feet upon a second 
staff, the ground at the foot of the second staff is 9"03 — 7-61 = V42 feet lower 
than at the foot of the first. And it should be noticed that this result is 
obtained without requiring any knowledge of the height of the object glass 
above ground, which varies each time the instrument is set up, by variation 
in the spread of the legs of the tripod, and is not quite conveniently 
measurable in ordinary instruments. The essence of the method is the use 
of the two staves, so that the height of the level itself is eliminated. 



In the above explanation of the use of the level we have 
made the important reservation " provided that the telescope is 
really pointing horizontal." The surveyor in the field cannot 
be continually revising the adjustment of his instrument, and it 
is characteristic of a good method of survey that the way in 
which the instrument is used should eliminate automatically 
errors due to imperfect adjustment. 

In the use of the level this end can be attained with great 
simplicity. All that is necessary is that the two staves should 
be placed at equal distances from the telescope. The reason 
for this will be seen at once, when we consider in what way the 
instrument is likely to get out of ad- 
justment. Reduced to its simplest 
parts, the level consists of a telescope 
fixed on an axis V, with a bubble B 
firmly fastened to the tube of the 
telescope. The axis V must be set 
up vertical, and the test of verticality 
is that the ends of the bubble B should 
not move along the scale when the 
instrument is rotated about V. The 
bubble may not be central on the scale, but so long as it does 
not move along the scale when the instrument is rotated, the 
axis is vertical. Hence the process of getting the axis vertical, 
which is required every time the instrument is set up, does 
not in theory depend upon the adjustment of the bubble or 
of the telescope. 



fi 



Fig. 12. 



Plate XII 



^L^'^ 



• i 



.v-f^^W 





2. 12 inch Y Level. 



xvelling. 



SIMPLE LAND SURVEY 



97 



Now if the bubble is not in the centre of its run when the 
axis is thus found to be vertical, the bubble is out of adjustment. 
And even if the bubble is in adjustment, it does not follow that 
the telescope below is parallel to it. 

These errors are adjusted from time to time by the methods given in any 
textbook on the use of the instrument. But they are apt to vary from day 
to day or from hour to hour while the instrument is in the field. The former 
does not afifect the results if care is taken to make the test of verticality of 
the axis as above, not that the bubble is central, but that it remains at rest 
when the instrument is turned about the vertical axis. But the effect of the 
second error is that the telescope is pointing" up or down at some small 
angle to the horizontal when the axis of rotation is made truly vertical. The 
resulting error of reading on the staff will be strictly proportional to the 
distance of the staff. Hence if two staves are at the same distance, the 
errors in reading will be the same, and the difference of the two readings, 
which is the quantity required, will be unaffected by the error. 




Fig- 13- 

Suppose, then, that we wish to run a line of levels from A to B. We 
mark out suitable stations K, Z, iJ/, ... in the line AB, for the staves. We 
set up the level midway between A and K, and find the difference of height 
of the ground at A and K. Then we set up midway between K and Z, and 
so on. Each difference of height is then independent of the errors of 
adjustment of the instrument, and it is not possible for the effects of these 
errors to accumulate, since they are automatically eliminated at each step. 

We should notice also that this process eliminates the effect 
of the curvature of the Earth. The line of sight of the telescope, 
being perpendicular to the vertical of the observer, is a tangent 
to the sphere and consequently passes higher and higher above 
the surface as it proceeds. Owing, then, to the curvature of the 

H. M, S. 7 



98 SIMPLE LAND SURVEY 

Earth, all staff readings are too high by a very small amount, 
which would become serious in time if sights were taken always 
forward from one station to the next, but is eliminated without 
conscious trouble by the method of setting up the instrument 
always half-way between the two staves. Thus no correction 
for the curvature of the Earth appears in ordinary levelling 
operations at all, even though they extend over hundreds of 
miles. Paradoxers who imagine that the Earth is flat are fond 
of quoting this as a confirmation of their idea. 

In a precisely similar way, there is no need to take any 
account of refraction if the level is always set up midway 
between the two staves. The effect of refraction will be to 
raise each staff in the field of view of the level, so that the 
readings are slightly too small. If observations were taken 
always to a forward staff this effect, extremely small for any 
one ray, would accumulate steadily, and would be very difficult 
to calculate. It is important, therefore, to notice that by the 
proper use of the two staves the effect of refraction is completely 
and automatically eliminated. 

Detailed sections. 

If we wish to make a section in great detail we may modify 
the above process without any damage to the essentials. 

The staff may be set up at any number of intermediate 
points between A and K, and the difference of height from 
A or K found. These observations will be affected by the 
instrumental error, but since the distances are short the effect 
will be small. And these observations will be used only to 
refer points between A and K to either ^ or ^ ; nothing will 
be carried on from them into the next section, which will start 
from K unaffected, as we have seen, by the instrumental error. 

The limitations of this process. 

We have been considering the process of running a line of 
levels as it may be used for particular purposes in a piece 
of isolated survey. The heights will be reckoned from a quite 



SIMPLE LAND SURVEY 99 

arbitrary datum, and will have no connection with mean sea 
level. 

The process of determining a general system of heights 
above mean sea level, as part of the organised survey of a whole 
country, will be considered in a later chapter ; see Chapter VI, 
page 133. 

And we should notice that the process here described is 
quite unsuited for a preliminary determination of heights and 
contours for an exploratory map. We shall deal with the 
processes proper to this purpose in Chapter V. 



CHAPTER V 

COMPASS AND PLANE TABLE SKETCHING 

In previous chapters we have dealt with the route traverse of 
the explorer ; and with the methods of mapping an isolated 
township or mining concession. We have to deal now with a 
problem of quite another kind : the production of the first 
attempt at the topographical map of a district, or of what is 
called in the language of military topography "a sketch." It is 
a map, in the sense that it covers all the area with a uniform 
degree of thoroughness, and does not merely draw a line across 
the country ; and it is a map also, in the sense that it aims at 
representing the whole topography of the ground, the relief as 
well as the plan. It is a sketch, in the sense that it is made 
with simple and portable instruments, rapidly, and with strictly 
limited means ; and it has no claim to great precision. 

Exploratory mapping of this kind has many uses. In war- 
fare it serves to produce temporary maps which shall serve all 
the purposes of a regular topographical map far in advance of 
the possibilities of a regular survey : such, for example, was the 
map of Burmah made in 1885 by two officers of Royal Engineers 
at the time of the expedition to Mandalay. In peace it may 
serve as a necessary preliminary to more detailed operations of 
survey, or to illustrate the work of a scientific expedition making 
a thorough study of an unmapped region, in geology, archaeology, 
or what not. And finally, in the teaching of geography it is 
admirably adapted to serve as a means of instruction in mapping 
which is within the powers of students, and can be executed 
in a limited time, with relatively simple instruments. 

Such a topographical sketch may be made with the prismatic 
compass and a simple instrument for measuring slopes, such as 



COMPASS AND PLANE TABLE SKETCHING loi 

the Watkin clinometer. Or it can be made with much greater 
accuracy, but at the expense of heavier and more costly tools, 
with the plane table and a clinometer of the pattern used on the 
Survey of India, and known familiarly as the Indian clino. In 
all the operations of survey the accuracy obtainable is limited 
by the time which can be given to the work, and the amount of 
baggage which it is possible to carry with the party. It is of 
great importance to have a clear appreciation of this principle. 
Much time may be saved by careful consideration before 
starting, of the degree of accuracy aimed at, and of the precise 
equipment necessary to obtain this in the most economical way. 
And much time is wasted by aiming at minute accuracy with 
rough and rapid methods, on the one hand ; or by using for 
what should be rapid work an instrumental equipment more 
suited to a higher degree of deliberation and precision. 

Whatever the instrumental outfit adopted, the same principle 
runs through all sketching, that a framework must be constructed 
by triangulation from a measured base, and that all detail must 
be hung upon this framework. If the position of one point of 
the triangulation can be determined in latitude and longitude 
by astronomical methods, such as we have already sketched in 
Chapter III, so much the better ; and again, if the sketch can be 
orientated correctly by an azimuth determined astronomically, 
again so much the better. But such determinations should be 
regarded as outside the limits of the methods of field sketching 
themselves. They add an excellent finish to the result, but they 
are not an essential part of the process, and we shall not deal 
further with them in these chapters. 

Compass sketching. 

The instruments are 

(i) the prismatic compass, of which the military pattern 
is by far the best, and also the most expensive, because it is 
fitted with arrangements for marching by night, which are not 
essential in work by day. (See Plate XIII); 

(2) the protractor, a graduated scale by means of which 
the observed angles are laid down on the drawing board, and 



I02 COMPASS AND PLANE TABLE SKETCHING 

distances are scaled off. Again, the military pattern, as described 
in the Manual of Map Reading and Field Sketching, is the best, 
and more expensive than simpler patterns, which can be used, 
though not so conveniently ; 

(3) a board on which drawing paper can be mounted, and 
which should have some kind of waterproof cover to protect the 
work from damage by rain ; 

(4) a good pencil, of the degree of hardness HH or 
HHH, which will take and preserve a fine point like a needle, 
and which should be protected in the pocket by a point 
protector. 

It may not be superfluous to observe, for the benefit of the 
beginner, that good quality in paper and pencil is essential to 
success. The paper has to stand a great deal of wear and much 
rubbing out ; and it will often get damp. At the end of work 
in the field it must be in condition to be cleaned up, inked in, 
and perhaps coloured. Only good drawing paper will be in this 
good condition when the sketch is finished ; inferior paper will 
have gone to pieces. Nor can any good work be done unless 
the pencil will take and keep a fine point ; and inferior pencils 
are the cause of endless waste of time and inaccuracy in work. 
Therefore do not grudge the few pence that will buy the best 
paper and pencils instead of the very inferior stuff in ordinary 
use. 

The compass. 

It would be tedious to describe in detail the features of an 
instrument which cannot be understood until the instrument 
itself is taken in the hand, but which then become almost self 
obvious. We will confine ourselves to some general remarks on 
compasses and their use. 

The compass card must be graduated right round from o'' to 
360°. Any other method of division is almost useless. The 
readings increase as one turns from magnetic north, reading 
zero, through east to south, and round again by west to north. 

It is essential that the compass, when not in use, should have 
the card raised off the point by the catch fitted for this purpose, 



Plate XIII 




I g S ^ »> I 2 — 



__ ,=iC«c» 



iJl^ M c. 



T. » ^ 3 h-^ O 'r*< O 
'^ 5 I A' ° 'I 



.^zm; 







The Service Pi'otractor. 



Compass Sketching. 



COMPASS AND PLANE TABLE SKETCHLNG 103 

or the card will rattle about, and the point of the needle on 
which it rests will be blunted. 

To try if the point is in good condition, open the cover out 
flat and lay the compass on a level table (as in Plate XIV). 
When the card has come to rest, turn the compass steadily in a 
horizontal plane, and see that the card remains at rest though 
the case is turned. If the point is good the card will not drag 
after the case but will remain almost unmoved. 

The prism, with one face ground into a lens, allows the eye 
to see at the same time the graduated compass card, and the 
distant object. To provide for differences in the focal length of 
different eyes, the prism is mounted on a slide, so that the card 
can be brought into clear focus for any eye. Place the compass 
at the edge of a level table, and draw out the prism to the end 
of its slide. Look in at the compass card, and gradually depress 
the prism until the divisions of the card are seen perfectly 
distinctly. Note the position of the prism in its slide, and if 
the compass is your own property make a mark to show where 
the prism should be placed without having to redetermine it on 
another occasion. 

In the use of the compass it is necessary to acquire the trick 
of seeing comfortably at the same time the distant object, the 
line in the cover of the compass superposed on it, and the com- 
pass card mingling with it, so that one may read the degrees of 
the card to which the line points. 

It is possible to see at the same time the distant object 
and the line close by, because they are viewed through the slit 
above the prism ; this slit restricts the pencils of light entering 
the eye to pencils of narrow angle, so that the eye can focus on 
them readily enough, though they come from objects at such 
different distances. 

It is possible to see the wire coming down over the compass 
card, because the view slit crosses the pupil of the eye from top 
to bottom. The light from the distant object enters the upper 
part of the pupil, and forms an image on the retina. The light 
from the compass card, reflected by the prism, enters the lower 
part of the pupil, and also makes an image on the retina. Across 



I04 COMPASS AND PLANE TABLE SKETCHING 

the centre of the field of view, where the illumination from the 
two sources is fairl}^ equal, the two images are visibly superposed, 
and one may see the wire as if it were actually coming down and 
cutting the compass card. To get the right effect, it is necessary 
that the two images should be nearly of the same brightness. 
Their relative brightness can be altered by moving the eye up 
and down along the slit, so that more or less of the pupil is 
exposed to the light from the object, and less or more to that 
from the card. The compass card, or dial, is engraved on 
mother-of-pearl in the best compasses, because that reflects a 
great deal of light, and gives an image of the card as bright 
as the image of the distant landscape, which is often very bright 
indeed. 

It is very common to see a beginner with the compass tilting 
it forward and downward, in the effort to see the two images 
plainly at the same time. This has the effect of dropping the 
card away from the prism, and putting the scale divisions out 
of focus. When one has determined the proper position for the 
prism, as explained above, the loss of focus is a plain indication 
that the compass is not being held level, which is dangerous, 
because the card may foul and give a quite wrong reading. 
Therefore it is well to be very sure about the proper position 
of the prism, and use this control over the tilt of the compass. 

Avoidance of local deflections. 

It is a commonplace that the compass becomes deranged 
and gives false readings if there is a mass of iron anywhere 
in the immediate neighbourhood. Yet it is very common to 
see beginners with the compass leaning against a bicycle or 
an iron gate, or taking bearings from the point of vantage that 
a bridge over a railway gives. Such mistakes are, of course, 
soon realised and avoided ; but it is not so easy to guard against 
less obvious sources of error, such as a water main under the 
road. 

Should there be any suspicion that abnormal attraction 
exists at the spot from which bearings are taken, it is easy 
to walk directly towards the objective, and repeat the bearing 
observation twenty or thirty yards further on. If there was 



Plate XIV 




I. Prismatic Compass. Mark VI. Opened out flat. 






Compass in use. 



3. Compass in position 
for use. 



4. Clinometer in use. 





5. Watkin Clinometer. 
Instruments for Compass SketcJiing. 



6. Interior of Clinometer. 



COMPASS AND PLANE TABLE SKETCHING 105 

local attraction at the first point, it will probably be different 
at the second, and the error will be detected. 

These remarks apply to strictly local attractions, such as 
are caused by fairly small masses of iron at close quarters. In 
some countries, such as South Africa, the whole ground is full of 
magnetic rocks, and the compass is practically useless. 

The compass sketch. 

The principle is exactly the same as in triangulating with 
the theodolite. A base is measured, and a framework of 
triangles is observed. The principal difference is, that the 
angles of the triangles are not determined as such, but as 
the differences between the observed magnetic bearings of the 
respective sides. Each side of a triangle is drawn as a line 
making a certain observed angle with the magnetic meridian, 
and is subject to the errors which are inseparable from these 
determinations of magnetic bearing. Hence we may expect 
errors of at least half a degree to occur with frequency. And 
a deviation of half ai degree is equivalent to a shift of one- 
twentieth of an inch at a distance of six inches, which is very 
much larger than the uncertainty of drawing. Hence we must 
realise that compass sketching is far from being an exact process, 
and must avoid putting too much time into a method which is 
incapable of giving anything like accuracy. Its merit is that 
it is quick, and that the instruments required are easy to carry 
about. 

Plotting the bearings. 

The observed magnetic bearings are plotted with the pro- 
tractor. The paper is ruled with parallel lines to serve as 
magnetic meridians, and one end of these lines is marked North. 
To protract a given bearing from any point the protractor is 
placed with its centre on the point, and its long side parallel 
to the meridians as drawn on the paper. If the angle is 
between 0° and 180° the ray will lie to the east, and the 
protractor will be placed so that it lies east of its centre. 
{Note : the centre of the protractor is the centre from which the 
angular divisions are struck, and is marked by a small arrow 



io6 COMPASS AND PLANE TABLE SKETCHING 

pointing to one edge.) If the angle is between i8o° and 360° 
the protractor is put down to the west of the centre, and an inner 
line of figures is used. All this is complicated to describe, but 
it may be learned by inspection of the instrument without any 
difficulty. To save mistakes, one should always ask oneself, 
Where roughly is the ray? If this is done, the protractor cannot 
be placed in the wrong position. 

The base. 

The necessary qualifications for a base are that it should be 
possible to see plenty of surrounding points from each end ; and 
that it should be practicable to measure roughly from one end 
to the other. Generally speaking, one has little opportunity for 
picking and choosing in selecting the base for a compass sketch. 
The sketch must be made without delay, and it is necessary 
to start without an elaborate search for a good base, which is 
always hard to find. The length of the base may be determined 
by pacing, or by measurement with a calibrated bicycle wheel. 
And it should be remembered that even if the base is ten per 
cent, wrong in length, the effect on the sketch is only that it is 
increased or diminished in scale ; it is not distorted, and if an 
opportunity occurs it is easy to make a new determination of 
some length and draw a new scale for it. 

In the Manual of Map Reading and Field Sketchijig the 
base is defined as a line carefully chosen and accurately mea- 
sured, upon which the accuracy of the sketch depends. This 
definition evidently needs qualification. In sketching and ex- 
ploratory work generally the first possible site must be chosen 
for the base, without delay for consideration of other and perhaps 
better sites which might be found on further reconnaissance. 
And the base will be measured, not accurately, but as well as 
the circumstances of the case permit. The accuracy of the scale 
of the sketch depends upon it, but not the shape. The unneces- 
sary stringency of the official definition might lead to a great 
waste of time in an operation where rapidity is often the first 
consideration. 

In pacing a base, it is often necessary to make some allowance 
for curvature of the way which the observer is compelled to go 



COMPASS AND PLANE TABLE SKETCHING 107 

from one end to the other. Care should be taken that the 
correction is not overestimated. On looking along a road, the 
divergences to right or left look very much more important 
than they really are. Divergences of fifty yards will make a 
road look very crooked, but they have very little effect upon the 
length of a mile of road between two points. Two or three per 
cent, reduction will be enough to allow for apparently quite 
considerable deviations. 

The measured length of the base is laid off by means of the 
scale on the protractor, giving hundreds of yards on the scale of 
two inches to the mile. 

The ruling points. 

The points that are chosen to make the triangles are termed 
ruling points. They will be natural objects such as church 
towers, isolated trees, haystacks, and so on. Trees are to be 
avoided as much as possible, because a tree that seems to 
be very easily distinguished from one point of view may be 
quite inconspicuous from another, or another tree may be mis- 
taken for it. 

Objects which can be seen but not occupied are also to be 
avoided, because to carry on the triangulation it is necessary to 
occupy points in succession. Such objects as steeples among 
trees, which cannot be occupied, and from the base of which 
nothing is visible, are not much good as ruling points. But 
they serve subsidiary purposes as " intersected points," as we 
shall see. 

The process of sketching. 

Select the base. Occupy one end of it. Take the bearing of 
the other end, and plot it. Then take and plot the bearings 
of any points round about that seem to be suitable for ruling 
points. Be sure that plenty of these points are taken at the 
start, for as the work proceeds one will find that some of 
the chosen points prove to be unsuitable, and must drop out 
of use. Unless plenty have been taken to start with, there is 
danger that too few may be left. 



io8 COMPASS AND PLANE TABLE SKETCHING 

Pace from one end of the base to the other, and scale off 
the distance from the protractor, making if necessary a suitable 
deduction for crooked pacing and slope. The further end of 
the base is now fixed. Take bearings to as many of the ruling 
points as possible. At least two points should now be deter- 
mined, one on each side of the base. Proceed to these, and 
continue the process of observing and plotting the rays to the 
ruling points. 

When the framework is thus built up, the second stage of 
the process begins. There will be important points, say at cross 
roads, which have not been fixed by intersections ; they will 
now be fixed by resection, that is to say, by taking bearings 
from each to two ruling points already fixed, and drawing rays 
back on those bearings until they intersect. The point of 
intersection will evidently fix the point under occupation. 

Round about the intersected and resected points, the detail 
is sketched in by eye estimation. This will not be very accurate, 
but it will be rapid, which is the most important consideration. 
And error cannot accumulate \o a serious extent, because the 
whole is controlled by the triangulation. The accomplished 
sketcher learns to economise in the use of instruments, and 
after the triangulation is done, he relies principally upon esti- 
mation for his intermediate detail. Also, he does not wait till 
the triangulation is done to begin the detail, but puts in as much 
as possible around each point that he occupies. 

Facility in sketching cannot be taught except in the field, 
and success depends upon cultivating an eye for country, so 
that the greatest possible economy of means may be practised. 
But it is possible to show certain ways of economising. 

For example, if it is important that a given road should 
be fixed as accurately as possible : it is sufficient to fix every 
alternate angle by resection, and to put in the intermediate 
angles by rays drawn down the road. Or again, if a village 
is to be sketched, it is usually wasteful of time to work right 
through it from one side to the other. Instead of doing so, work 
round the outside of the village, fixing points on the roads that 
approach it, and the directions of those roads. Having laid 



COMPASS AND PLANE TABLE SKETCH LNG 109 

down the roads leading to the village, it will generally be easy 
to sketch the whole of the necessary detail of the village itself 
without being obliged to make any instrumental fixings inside. 
Many time-saving methods such as this will be learned by 
experience. 

The clinometer. 

This instrument measures the angle of slope. As with the 
compass, it is tedious and unnecessary to describe the instru- 
ment minutely, since its use is almost self-evident when the 
instrument is taken in the hand. (See Plate XIV.) But a few 
principles that are not quite evident may be examined here. 

In the first place, remember that an error in the zero of the 
clinometer is fatal to success in its use. If the compass has an 
error of zero, the whole sketch is slewed round by that amount, 
but no further harm is done. But if the clinometer has such an 
error, that is to say, if the clinometer reads angles of elevation 
too small, and angles of depression too large by the same 
amount, the effect on the differences of height measured with 
the instrument are very serious. The difference of height be- 
tween the top and the bottom of a hill would seem to depend 
upon whether the observations were made from the top or the 
bottom. 

Hence the state of adjustment of the clinometer should be 
examined every day that it is used, for the process takes only 
a minute or two. Observe the same ray from opposite ends. 
Suppose that it reads Elevation 2° at one end, and Depression 3° 
at the other. Then evidently the clinometer reads half a degree 
low, and a correction to allow for this must be applied to all the 
readings made with it. It is better to determine this correction 
and apply it mentally, than to try and adjust the instrument 
by opening it up and turning the adjusting screw. This is a 
tedious process ; and it is apt after a little to leave the screw 
loose, so that the error varies with every jar that the instrument 
receives. 

The clinometer measures the elevation or depression of one 
point as seen from another, in angle. To convert this into 



no COMPASS AND PLANE TABLE SKETCHING 

difference of height in feet we must know the distance between 
the two points in yards. This is taken from the sketch by- 
means of the scale of yards on the protractor. We then apply 

the rule 

/horizontal distance in yards, 

. divided by twenty, and 

Difference of height m feet = ^ ,^. ,• j i ^u i 

^ I multiplied by the slope 

V in degrees. 

The proof of this rule is very simple. A slope of one degree is equi- 
valent to a rise of one foot vertically in a distance of 57"3 feet horizontally. 
Since 57"3 is an awkward number to deal with mentally, we substitute 60, 
which is near enough to correspond to the accuracy of the whole process. 
The 60 becomes 20 because the vertical intervals are measured in feet, while 
the horizontal distances are measured in yards, by old standing tradition. 
The rule now becomes evident. 

It is easy to see that the process is the more accurate the shorter the 
distances involved. Suppose the slope is one and a half degrees, and 
the distance 2460 yards. The vertical interval is 2460 divided by 20, 
and multiplied by r5, or 185 feet. But suppose that the slope had been 
one and three quarter degrees ; the vertical interval would then have 
been 215 feet. A quarter of a degree, which is less than the instrument 
can give with certainty, makes a difference of 30 feet in the result, and 
this difference is evidently proportional to the horizontal distance between 
the two points. At a thousand yards a quarter of a degree makes a dif- 
ference of twelve feet, so that it is useless to expect to obtain heights with 
the clinometer which are correct within a few feet. In gently undulating 
country, where the distance from point to point will tend to be large, while 
the uncertainty in the measure of the slope is an important part of the 
whole quantity, the results given by the clinometer are very likely to be 
inconsistent and confusing. 

Assumed datum height. 

In making a compass sketch it is not commonly the case 
that the height of any point above sea level is known. It is 
then necessary to make an intelligent assumption of some height 
to start with. This is called the assumed datum, or given 
height; and all others are reckoned from it as zero. All figures 
of heights entered on the sketch should be referred to this 
datum; they should never be entered as differences from some 
other point, but always as heights above sea level or datum, 
with the assumed datum. 



COMPASS AND PLANE TABLE SKETCHING in 

Sometimes it is convenient to determine the height of the 
top of a tower which may be visible though the base is not. 
Such heights should be entered in a list on the edge of the 
sheet ; no figure, except the height above sea of the ground 
itself, should ever be written alongside the object on the 
sheet. 

Contouring with the clinometer. 

The most ready method of showing the relief of the ground 
is by sketching the contours or form lines : the latter being the 
rougher and more sketchy attempts at the former. Since time 
is always of the greatest importance in this class of work we 
must be careful that we limit the use of the instrument to the 
smallest possible number of observations, and that these observa- 
tions are so disposed that they produce the greatest effect. 

The first step is to obtain the heights above sea, or above 
datum, of the ruling points ; this gives a framework of spot 
heights upon which to construct the contours. We have already 
seen how the height of one point is found when the height of 
some other visible point is known. 

The second part of the process is to find how the contours lie 
round about one of these spot heights. Suppose that the ground 
slopes away uniformly in a given direction, at a slope of 2°. 
What is the interval in yards on this slope between contours 
having a given vertical interval ? The question is easily solved 
by inverting the relation given above, and writing it 



Horizontal interval in yards = 



^vertical interval in feet, 
multiplied by twenty and 
divided by the number 
of degrees in the slope. 



Thus if the vertical interval adopted for the contours is 25 feet, on a slope 
of 2° the contours are spaced at a distance of 250 yards apart. 

Suppose then that the spot height is 284 feet. Down the slope the first 
contour is that for 275 feet. Here the vertical interval from the spot height 
to the first contour is 9 feet, and its horizontal distance is therefore nine 
twenty-fifths of 250 yards, or 90 yards. Take the protractor and scale off 
90 yards along the line which marks the direction in which the slope has 
been measured. This brings us down to the 275 contour ; thence scaling off 



112 COMPASS AND PLANE TABLE S KETCH LNG 

successive distances of 250 yards we obtain points on the 250, 225, 200, and 
succeeding contours, so long as the slope remains uniform. 

Repeating this process in a different direction we obtain other points on 
the same contours ; and these are eventually joined up by sketching. 

It is clear that this process may be very wasteful of time 
unless care is taken that the lines of points so determined are 
dominant in the construction of the contours. It is almost 
impossible to lay down in a book the principles of economy in 
contouring which can be learned only by practice in the field. 
But one general rule is clearly useful. Run these lines of points, 
or contour ranges, as we may call them, along the ridges and the 
valley bottoms. With a range along each crest and one up the 
floor of the valley it is possible to sketch the whole of the valley 
contours without the possibility of going far wrong. 

Beginners are apt to find this process of contouring with a 
clinometer somewhat confusing, and are to be seen working out 
the necessary small calculations on paper. This should never 
be required. The student should train himself to do all the 
calculation mentally, always remembering that the process is at 
best only a rough one, and that quantities of a foot or two have 
no real significance. Otherwise it would not be legitimate to 
use the convenient whole number 20 in place of the more 
accurate I9"i. 

The older pattern Service protractor has scales which show 
the horizontal distances between contours for each degree of 
slope on two different scales. These are not of much use, since 
it is difficult to interpolate for the fractions of degrees. It is far 
better to accustom oneself from the start to work out mentally 
the distances in yards, and to take these off the scales of yards 
found on the protractor. 

Height above ground of the observer's eye. 

In strictness it should be necessary to take account of the 
fact that the observations are made from a point about five feet 
above ground. On short rays one may take sufficient account 
of this by observing to some object such as a bush or the top of 



Plate XV 




Plane Table and Sight Rule: School of Military 
Engineering pattern. 




2. Indian Clinometer on Plane Table. 



I IS f run tents for Plane Tabling: 



COMPASS AND PLANE TABLE SKETCHLNG 113 

the hedge, which is judged to be of about the same height as the 
observer. On long rays the effect of neglecting this precaution 
becomes inappreciable. 

The plane table. 

The plane table is unique among survey instruments in that 
it enables the surveyor to draw a map without measuring any 
angles or doing any numerical work, except in the contouring. 
The plane table is, in fact, a drawing instrument, by means of 
which the map is drawn in the field without the intervention 
of any angle measuring instruments. It is exceedingly well 
adapted for rapid survey, and is very much used for making 
maps in a hurry, as may be necessary in military operations 
in an unmapped country, or during any rapid exploration. 

The instrument consists of a drawing board covered smoothly 
with drawing paper, and mounted on a light but rigid tripod, 
upon which the board can turn, and can be clamped in any 
position desired. The accessories are : 

(i) a sight rule, preferably of boxwood, having folding sights 
which can be turned up at each end. One sight has a narrow 
vertical slit in it ; the other consists of a vertical wire stretched 
across an open frame ; 

(2) a trough compass, which is a long compass needle 
mounted in a narrow box, with a short scale at each end. When 
the needle is pointing to the centre of the scale at each end it is 
parallel to the sides of the box ; 

(3) a hard, well pointed pencil of good quality. 

The sight rule should be graduated along one edge in inches, 
and along the other with a scale of yards corresponding to the 
scale on which it is proposed to work : very frequently the scale 
of two inches to one mile. 

The plane table has two principal uses, which must be 
distinguished one from another. It can be used to produce a 
complete map, entirely by its own resources, without the use 
of any other instrument than the accessories which normally 
accompany it ; the triangulation can be made with it, and the 
whole detail filled in with it. Or it can be used to fill in the 

H. M. S. 8 



114 COMPASS AND PLANE TABLE SKETCHLNG 

detail after the triangulation has been made with the theodolite. 
The first is the use to which it is put in rapid and exploratory 
mapping ; the second is its role in the more leisurely operations 
of the precise survey of a large country, such as India or 
South Africa. 

We will begin by considering its use in rapid survey or 
reconnaissance. 

Graphical plane tabling. 

By graphical we mean that the plane table is to be used as a 
drawing instrument, to make the complete map without other 
instrumental aid. Both triangulation and detail are to be done 
with it. 

The principles of the triangulation are naturally the same as 
those which we have already considered in compass sketching, 
and it will not be necessary to repeat that the process consists of 
measuring a base, and building up on it a framework of well 
proportioned triangles. 

Measurement of the base. 

The base must be chosen in as open and level a piece of 
country as can be found, and its ends must be marked in some 
conspicuous way, so that they are visible one from the other, and 
from the surrounding points which will be occupied in succession 
to extend the base and start the triangulation. Plane tabling is 
a much more accurate process than compass sketching, and a 
correspondingly greater degree of care is required in choosing 
the ground for the base. 

If time allows, beacons may be erected to mark the ends of 
the base and the ruling points. But beacons are by no means 
necessary in a rapid graphical triangulation, and we shall suppose 
that they are dispensed with. But we shall remember always 
that the more accurately defined the ruling points are, the more 
accurate will be the result. 

Let us take two solitary trees or posts on a straight open road, 
being careful to see that they can be identified with certainty from 
the surrounding country, and not confused with neighbouring 



COMPASS AND PLANE TABLE SKETCHLNG 115 

trees or posts. We shall get the base as long as possible : 
perhaps from half a mile to a mile long. 

We have now to measure the base, and the more accurately 
the better. If chain or steel tape is available, it should be 
used. Failing these, a good deal can be done with a carefully 
calibrated bicycle wheel ; and failing any kind of measuring 
instrument the base must be paced. The error of the result may 
in this case be three or four per cent. But this affects only the 
scale of the map, not the relative configuration of points marked 
upon it. And for many purposes the exact scale of the map is 
not very important, so long as the topography is correct. 

Plotting the base on the plane table sheet. 

The base is measured in yards, and the length corresponding, 
on the scale of the intended map, is taken from the scale of yards 
on the edge of the sight rule. Consider the position of the base 
in the area which is to be mapped, whether it is to the centre or 
to the side ; draw a fine line with the sight rule in the convenient 
position, and lay off on it the length representing the base 
measure, making fine perforations in the paper with the sharp 
hard point of the pencil, so that other rays may be passed 
accurately through these points when required. It is well to 
draw continuations of the line on which the base is to be laid off, 
at each end of the sight rule, so that the rule may be laid down 
accurately along its original direction in a subsequent step of the 
process ; usually the base line is so short that the rule cannot be 
laid down on it again with any great precision. 

Call the ends of the base A and B. 

Set up the plane table at ^, as close as possible to the mark. 
In plane tabling on the scale of two inches to one mile, one 
hundredth of an inch represents about eight yards on the ground, 
so that divergences of a yard or two from the exact position of 
the station are hardly visible upon the map, being within the 
limits of error in drawing. Lay the sight rule along the line of 
the base on the table, and turn the table till the line of sight falls 
on B ; then clamp the table. Beginners find some difficulty in 
sighting along the rule, and are seen looking sideways in very 
awkward positions. It may be helpful to say that the correct 



ii6 COMPASS AND PLANE TABLE SKETCHING 

position for plane tabling is as nearly as possible the correct 
position for wicket-keeping in cricket. 

Beginning the triangulation. 

The last process has set the plane table. That is to say, the 
base line drawn on the table is parallel to the base line on the 
ground. And the point A on the table is over the corresponding 
point on the ground. We can therefore draw the ray from A to 
any other point by placing the sight rule so that its edge passes 
through A on the table and is directed to the point C on the 
ground. A convenient way of manipulating the sight rule is to 
stand the pencil (hexagonal) with one corner on A, holding it 
with the left hand, and with the right hand swing the sight rule 
about this corner as a pivot until it is sighted on the point C. 
Then carefully rule a line passing 
through A towards C. It is essential \/ \/ 

that the pencil have a fine needle-like ^ /\ ' ' 

point, and that it be held carefully to 
make a line really parallel to the edge 
of the rule. It is not necessary to 
draw the whole line AC. Make an 
estimate of the distance of C\ suppose 
it is one mile and a half This will 

be three inches on the paper if we are b a 

working at two inches to one mile. 
Draw then a piece of the line only, 
about three inches from A. If the 
piece is not long enough it may be 
lengthened later. But it should be 

Fig*. 14. 

remembered that all the rays drawn 

must be rubbed out in the end, so that it is economy to draw 

as little of the ray as will serve its purpose. 

In the same way draw rays to other points D, E, F ... which may be 
useful as ruhng points. We leave A with the knowledge that all the points 
C, D, E, F., ... which are to be mapped lie somewhere on the lines AC, 
AD, ... which have been drawn ; their precise positions will be determined 
by other rays drawn from B ... intersecting these "first lines. 

Now move the table to B, and set it by laying the sight rule along the 
line BA and turning the table until the rule is set on A. The table is now 



COMPASS AND PLANE TABLE SKETCHING 117 

set ; that is to say, it has been moved from A to B parallel to itself, so that 
any line already drawn on the table is parallel to its position on the ground. 
Having set the table we draw rays BC^ BD, ... to the points already observed 
from A, or to as many of them as are visible from B ; and thus C, /?, ... 
are fixed. 

Two points, one on each side of the base, must be fixed by the intersections 
of two rays only, from A and B ; and it is important to see that these 
intersections are as nearly at right angles as possible. A good intersection 
is a blunc intersection. When the rays cut one another acutely a small error 
in either will make a good deal of difference in the place of the intersection. 

From C and D we proceed to fix other points ; and we must not accept 
any point as well fixed unless it depends on three rays which intersect in 
a point without visible deviation. Working on in this way we build up a 
framework of triangles upon the base in the same way as we did in compass 
sketching. But the accuracy of the result is considerably greater. 

Choice of stations. 

Only experience in the field can teach how to select the 
stations of a triangulation with advantage ; and the selection will 
naturally be governed by the nature of the country. The stations 
must fulfil many conditions : 

(i) they must be in commanding positions, so that stations 
all round are visible from them ; 

(2) they must be well marked natural or artificial objects, 
such as a sharp summit of a hill, or the trunk of an isolated tree, 
or the top of a tower. The top of a tree surrounded by low 
growth, and the point of a steeple, are not suitable objects to 
select for the continuation of the triangulation, since they 
cannot be occupied in their turn ; 

(3) they must make well conditioned triangles, with no very 
acute angles. 

It will often happen that without a preliminary reconnaissance 
and occupation of the proposed stations, the surveyor will be 
deceived. A point ahead may appear to be an admirable station, 
but when it is occupied it may be found that further progress is 
obstructed by natural or artificial obstacles which could not be 
seen from the last station. It is therefore advisable to draw rays 
to more points than are really required for the triangulation. 
This will allow for the dropping out of stations which prove in 
the end to be unsuitable. 



ii8 COMPASS AND PLANE TABLE SKETCHING 

It is one of the great advantages of plane tabling that a great 
number of rays may be drawn with very little trouble, so that 
superfluous rays need cause no regret, and the survey can go 
ahead without preliminary reconnaissance. In a theodolite 
triangulation the case is very different. Here a reconnaissance 
is absolutely necessary, for selecting and beaconing the stations, 
and by far the best kind of reconnaissance is a plane table 
triangulation. 

The use of the triangulation. 

When the triangulation is complete our plane table sheet is 
covered with a series of rays intersecting in points, which are 
conspicuous points about the country, tops of hills, isolated trees, 
church towers, and so on. The triangulation is the skeleton of 
the map, but the visible map is not yet begun. It may be that 
we do not propose to go any further immediately. We have laid 
out the framework of triangles ; from this we can select the 
particular scheme best fitted for observation with the theodolite, 
and we are then ready to beacon the country for the deliberate 
observation. But if time presses, and we wish to have an 
approximately complete map as quickly as possible, we must 
dispense with the precise triangulation, and proceed at once to 
fill in the detail of our plane table sheet. 

The map is to show the natural features of the country, hills, 
valleys, and rivers, and the artificial features, railways, roads, and 
towns. These, the most important topographical features, are 
not as a rule marked by upstanding conspicuous points suitable 
for triangulation stations, while, on the other hand, very excellent 
triangulation stations, such as isolated rocks or trees, are not 
features that will eventually appear at all upon the topographical 
map. Our skeleton, then, is no part of the map proper, and is 
destined to disappear in the end, leaving no sign of the rays 
which constructed it, and only the small triangular signs to mark 
the stations which were used. 

Accuracy of the graphical triangulation. 

The sight rule can be set upon an object with an accuracy of 
two or three minutes of arc ; this is readily seen if we consider 



COMPASS AND PLANE TABLE SKETCHLNG 119 

that the diameter of the sun or moon is about thirty minutes of 
arc, and that they are very large objects to set upon if we view 
them along the sight rule when they are near the horizon. It 
is not hard to set with an accuracy less than one tenth of the 
diameter of the moon. On the other hand, the error of a 
compass bearing, observed without a tripod or other rest for the 
compass, is likely to be at least half a degree. Hence the rays 
drawn on the plane table are very much more accurate than 
those plotted from compass bearings. By increasing the bulk 
and weight of our apparatus we have much increased its 
accuracy. This is a simple example of the general principle 
that the accuracy of any survey process is limited by the weight 
one is prepared to carry and the money to be spent. 

Difference in principle between plane tabling and compass 
sketching. 

It is important to note the difference in principle between 
plane tabling and compass sketching, as regards the construction 
of the triangulation. In compass sketching each ray is plotted 
independently as an absolute magnetic bearing. In plane tabling 
the board is set up at each new triangulation point by sighting 
back with the sight rule on one of the other points already well 
fixed. The process depends only on the care with which the 
settings are made, and the stability of the table. Up to this 
point the compass does not enter at all into the work ; and we 
are free of the various errors, such as local attraction and daily 
variation of the compass, which limit so much the accuracy of 
compass work. 

Intersected points. 

The stations of the triangulation are perhaps two or three 
miles apart. As each one is occupied we take advantage of its 
commanding position to draw rays to all the conspicuous objects 
round about — not with the idea of occupying them in turn as 
triangulation stations, but in order that they shall be well fixed 
by intersecting lines. In this way a great number of steeples, 
chimneys, well marked trees, and such objects, will have been 
put in on the plane table sheet. These are called Intersected 



120 COMPASS AND PLANE TABLE SKETCHING 

points. In what follows they serve as auxiliary to the principal 
points of the triangulation ; and like them, are destined in great 
part to disappear from the finished map, since they are often of 
no topographical importance. 

The use of the trough compass. 

At some point of the triangulation, when the table is 
orientated by setting on another triangulation point, the trough 
compass is taken from its case and laid on the table, with the 
end of the needle which is marked with a cut toward, the^north. 
The compass is turned until the needle points to the zero of the 
scale at each end. The needle now lies in the magnetic meridian, 
and the sides of the box, being parallel to the line of zeros of the 
scales, are also in this meridian. Draw pencil lines along the 
sides of the box, and mark the north end. (See Plate XVI.) 

Now at any point whatever of the ground we are able to set 
up the plane table in approximate orientation. Set up the 
table ; take out the trough compass and place it on the compass 
lines drawn as above, taking care that the north end of the 
needle lies to the end marked north. Then turn the table until 
the needle points to zero. The table is now orientated as 
accurately as the compass permits, that is to say, within about 
a quarter of a degree, unless there are magnetic disturbances 
about. 

The purpose of this orientation by compass is to facilitate 
the process of resection which follows. 

Filling in the detail. 

Up to the present we have been fixing well marked points 
by drawing intersecting rays from other points previously deter- 
mined. When a sufficiency of these have been fixed, we begin 
the new operation of putting in the important topographical 
detail, the roads, fords, railway bridges, and so on, which are 
inconspicuous objects in general, as viewed from the ruling 
points, and cannot be determined by intersections. But, on 
the other hand, the ruling points should be quite conspicuously 
visible from them ; and if three are visible we can (with certain 
limitations to be discussed at a later stage) set up the plane table 



Plate XVI 




I. Trough Compass and Case. 







Plane Table and Telescopic Alidade : United States 
Coast and Geodetic Survey. 



Instruments for Plane Tabling, 



COMPASS AND PLANE TABLE SKETCHING 121 

and determine the place on the map, by the process known as 
resection. Perhaps retrosection would have been the better 
term, since the process consists of drawing rays backwards from 
the ruling points. A point determined by resection is often 
called a plane table fixing. 

Plane table fixing by resection. 

Whenever three ruling points, suitably disposed, are visible, 
a plane table fixing may be made. The conditions for suit- 
ability are 

(i) that the points are not too close together, neither is one 
nearly opposite another ; 

(2) that they do not lie nearly on a circle passing through 
the point which is to be fixed. 

The reason for these restrictions will appear in due course. 

By means of the trough compass set up the table in approxi- 
mate orientation. Set the sight rule so that it is directed to one 
of the points, while its edge passes through the place of this point 
on the table ; and draw a ray back. Do the same for the other 
points. If the three ruling points were correctly fixed, and the 
table in correct orientation, the three rays would meet in a point, 
which would be the point on the table corresponding to the place 
where the table stands on the ground. 

More often than not the three rays do not meet accurately 
in a point, but make a small triangle, which is called the triangle 
of error. This is not due primarily to any error in the positions 
of the ruling points, nor to inaccuracy in drawing the rays, but 
to error in the orientation of the table as set up by the trough 
compass. The compass cannot be relied on to within half a 
degree at the best ; and there may be iron pipes under the road, 
affecting it. Moreover, owing to the convergence of the magnetic 
meridians, lines drawn alono; the magnetic meridians at different 
parts of the sheet will not be accurately parallel to one another. 
In dealing with the triangle of error we assume that the whole 
of the error is due to this faulty setting up of the table. 



122 COMPASS AND PLANE TABLE SKETCHING 

Solution of the triangle of error. 

It might be supposed that when there is a triangle of error, 
the true place which we are trying to fix would be at the centre 
of gravity of the triangle. But this is entirely wrong. It is not 
necessarily inside the triangle at all, as will be seen from the 
following considerations. 

Let A, B, C he our three ruling points on the map, and O the 
point in process of fixing. If the table is not rightly orientated 
it is rotated about the point where it stands on the ground, and 
we may represent this by turning it in our figure about the point O 
on the map, so that A, B, C are moved to A', B', C on the table. 







Fig. 15- 

Now draw the rays again. Since the real points are distant, the 
new rays will pass through A', B', C, and will be parallel to the 
old rays. They will intersect to form a triangle ; but O is more 
likely to be outside than inside the triangle. 

The student is advised to draw a few cases for himself. He 
will then easily understand, and be able to prove, the following 
rules for constructing the point O from the triangle of error. 

Rule I. If the table is set up within the triangle formed by 
the three points on the ground, the place of the table on the map 
will be inside the triangle of error ; if not, it will be outside. 



COMPASS AND PLANE TABLE SL< ETCHING 123 

Rule 2. The point O will lie always to the right or always to 
the left of the three rays, as one looks along them to the points 
from which they are drawn. (It will be seen that Rule i is 
really included in Rule 2, but it is convenient in practice to 
state the two separately.) 

Rule 3. The perpendicular distances of O from the three 
rays are proportional to the distances from the table of the 
corresponding points on the ground. 




To take an example as in the figure. Let the three rays be 
drawn as shown, and let O be outside the 
triangle ABC on the ground. 

By Rule i O on the map is outside the 
triangle of error. 

By Rule 2 it cannot be in either of the 
sectors marked by shading. 

By Rule 3, for the proportions of the per- 
pendiculars, it cannot be in the remaining 
right-hand sector, but must be in the left, 
at the point indicated. p.^ . 

The method of making a plane table fixing is complicated to 
explain. After a little instruction and practice in the field it 
is perfectly easy and rapid in execution. And it is the most 
ordinary operation in plane table survey. Point by point plane 
table fixings are made all along the roads, rivers, and railways ; 
and thus the detail of the map is quickly filled in. It will be 
understood that only practice in the field can show how to 
economise effort by making the fixings at the points where they 
are most effective. No written explanation can give an eye for 
country. 

Check on the solution of the triangle of error. 

If the triangle of error is large, or the surveyor inexperienced, 
it is well to have a check on the accuracy of the solution that 
has been made. This is very simple. By hypothesis the triangle 
has arisen from bad orientation of the table. When the first 
solution has been made, lay the sight rule along the point which 



124 COMPASS AND PLANE TABLE SKETCHING 

the solution gives, and one of the ruHng points which has been 
used. Look along the sight rule, and the distant point will be 
off the cross wire. Unclamp the table, and turn it till the point 
comes on. Then clamp, and repeat the resection. This time 
the triangle of error should be exceedingly small, if not an exact 
point, and the solution should give a result very near the first 
solution. If it does not, something is wrong. Inspection of the 
solutions will probably show that an error has been made. If, 
however, the solutions are made according to the rules, and yet 
give discordant results, then it is probable that there is some 
error in one or more of the ruling points, and this must be put 
right by revisiting the triangulation points until all is verified. 
It is no use trying to get good results from resections until the 
ruling points are really laid down in their true places. 

Case in which the solution fails. 

The solution fails when the point which is to be fixed lies on 
or near the circle passing through the three chosen ruling points. 
If it lies exactly on the circle the solution becomes quite inde- 
terminate. However wrong the orientation of the table may be, 
the three rays meet in a point, and it will appear that a perfect 
result has been achieved. But turn the table round into another 
orientation, and repeat the process. Again the three rays meet 
in a point, though quite a different point. This curious result 
depends on the well-known proposition that all angles in the 
same segment of a circle are equal to one another. 

If the point to be fixed lies very nearly on the circle, the 
result is very nearly as indeterminate, and no good solution can 
be obtained. Great care must be taken, therefore, that the three 
ruling points are chosen so that there is no chance that the 
problem may become indeterminate in this way. If the three 
points in order are A, B, C, try to ensure that B is nearer than 
either A or C. The circle passing through them will then lie 
far away from the point which is occupied, and the solution will 
not fail. 

Remarks on the part played by the compass. 

It is essential that the beginner should plainly understand 
the part played by the compass in this operation. The compass 



COMPASS AND PLANE TABLE SKETCHING 125 

is an uncertain instrument, and cannot be relied upon to give 
the orientation right within half a degree. For this reason the 
orientation of the plane table, when it is set up by compass for 
the resection, is always to be considered suspect. The size of 
the triangle of error is an indication of how much it is wrong ; 
and the solution of the triangle of error eliminates completely 
the effect of the wrong orientation. In fact the compass is used 
only for convenience, in order that the triangle of error may be 
small. The compass is not indispensable, and if it is lost or 
broken the process may be worked without it. Set up the table 
by estimate in about the right orientation, and make a solution. 
The triangle of error will be very large, but it can be solved 
approximately. Re-orientate the table on the result of the first 
solution, and make a second. This will come out with a very 
much smaller triangle. If necessary repeat the process again, 
and this time the result will be satisfactory. 

It is clear from this that the role of the compass is quite 
subordinate, and that any error in it will not affect the ultimate 
accuracy that is achieved. 

The plane table a modern instrument. 

The discovery of the right use of the plane table is of 
comparatively modern date, and its credit belongs to the Survey 
of India. The instrument itself is ancient ; but so long as it 
was employed only for fixing points by intersection, or so long 
as it was set up by compass, and resections were made by two 
rays only^ it was not a very valuable instrument The intro- 
duction of the method of resection by the solution of the 
triangle of error made it at once an instrument of precision, 
unexcelled for convenience and rapidity of work. 

Plane table traverse. 

In closely wooded or otherwise obstructed country the 
method of resection may fail because three points cannot be 
seen. In such cases it is necessary to make a plane table 
traverse through the awkward area. 

Suppose it is required to map a road passing through a 
village. Make a plane table fixing on the road as near the 



126 COMPASS AND PLANE TABLE SKETCHING 

village as possible. Draw a ray to represent the direction of 
the road to the furthest visible point. Take up the table, leaving 
a mark to show where it stood, and pace to the forward point ; 
then measure off the paced distance along the ray which has 
been drawn. This will give the place of the forward point with 
fair precision. Set up the table there ; orientate it on the back 
point ; draw a new ray forward as far as possible ; and proceed 
as before. In this way the road can be drawn in, leg by leg, 
until it comes out again into open country, and the whole can 
then be checked by a plane table fixing. Probably the result of 
this will not agree with the position as carried through by the 
traverse, and it will be necessary to adjust the traverse to make 
it fit on to the plane table fixings. 

Adjustment of a traverse. 

Suppose that the traverse ABC...M ends at M, and that a 
plane table fixing at this end makes the position M'. It is 




Fig. 17. Adjustment of traverse. The full line is the original; the dotted 
line is the traverse adjusted to close on M' . 

required to adjust the traverse so that it closes on M'. Join 
MM' and draw lines parallel to 3LM' through each angular 
point of the traverse. Each of these points must be moved 
along its corresponding parallel by a fraction of the length MM' 



COMPASS AND PLANE TABLE SKETCHING 127 

proportional to the distance from A. This rule is of course 
arbitrary. It is not pretended that the result is precisely right ; 
but some systematic method of adjustment is required, and this 
appears to be the best. 

In practice the rule is simplified thus : Suppose there are ten 
legs to the traverse, ending at B, C, D, ... M. The B is moved 
one tenth of MM', C is moved two tenths, and so on, which 
brings M to M' ; and the traverse is adjusted. 

Heights and contours. 

For rapid and approximate work the heights and contours 
can be done with the Watkin clinometer, precisely as in compass 
sketching, and it is not necessary to repeat here what we have 
already said on pages 109- 112. 

For more accurate work the relative heights of the triangula- 
tion points are determined with the theodolite, and other heights 
are determined from them with the Indian pattern Clinometer, 
commonly called the Indian clino. We will defer a description 
of this instrument to the chapter on Trigonometrical Survey. 
See Chapter VI, page 161. 

Characteristic signs, and style of drawing. 

The appearance of the finished sheet will depend very much 
upon skill and care in draughtsmanship, and particular attention 
must be paid to the conventions which are adopted for the 
representation of both natural and artificial features. These 
conventions vary to some extent with the style of the survey — 
for rapid reconnaissance work the style is less elaborate than in 
the more leisurely operations of an organised survey. For the 
former, see the characteristic sheet in the official Manual of Map 
Reading and Field Sketching. For the latter, reference may be 
made to the margins of published maps, or to the characteristic 
sheets published by the Survey departments. 

Elaborate plane tables. 

The instrument that we have described is the pattern adopted 
in the British military service, and carried by field companies of 
the Royal Engineers. It is set up level by estimation only, and 
its sight rule has only plain sights, without any optical aid. 



128 COMPASS AND PLANE TABLE SKETCHING 

Much more elaborate instruments have been introduced, 
with levels and levelling screws to set the table truly horizontal ; 
with telescopes on the sight rules (then called telescopic 
alidades), and other refinements which add very much to the 
cost and the weight of the instrument, while detracting very 
much from the convenience and rapidity of handling it. (See 
Plate XVI.) Opinion is divided as to the utility of these 
elaborations, and it is not possible to decide dogmatically for or 
against them. But there is one consideration which is weighty 
against the elaboration of the plane table. The work is done on 
a sheet of paper ; and however carefully this may be seasoned 
and mounted on linen, it is subject to distortion by moisture, 
especially in the tropical climates where it is so much employed. 
This is an argument in favour of keeping the instrument as 
simple as possible, and not trying to obtain with it too minute 
an accuracy. 

It should be said, however, that within the last few years 
there has been a change in the opinion formerly held at the 
School of Military Engineering, Chatham. The Close-Brooker 
telescopic alidade, with a parallel rule attachment, has come into 
ordinary use, and it is found that the increased accuracy which 
may be obtained with it compensates for the greater weight and 
cost. 

Limitations to the accuracy of graphical plane tabling. 

The method of graphical plane tabling discards numerical 
measurement and computation, and relies upon pointing, 
generally without optical aid, and upon drawing. Every line 
drawn upon the table is liable to be in error by an amount on 
the border line of visibility ; these errors accumulate until they 
become quite considerable, and cannot be tolerated on a map 
with any pretensions to accuracy. 

Further, there is a difficulty to be discussed more in detail 
later — the question of the projection, and the effects of the 
Earth's curvature — which make it impossible to carry on a 
survey continuously through a number of sheets, and trouble- 
some to derive latitudes and longitudes of the places mapped. 

Hence plane table triangulation has strictly limited uses. It 



COMPASS AND PLANE TABLE SKETCHING 129 

is admirable for exploratory and reconnaissance work, but it 
cannot be used as the basis of a deliberate survey. This must 
depend upon theodolite triangulation and calculation. 

But as an instrument for filling in the detail of a precise 
triangulation the plane table is unsurpassed, and we shall have 
further occasion to consider it. 

Tacheometer and Subtense Traverses. 

The principle of subtense measurement is simple. It is 
required to measure the length of a ray over rough country 
unsuitable for ordinary traversing. At one end of the ray two 
marks are erected in a line at right angles to the ray. Their 
linear distance apart is measured by the party who erect them ; 
and their angular distance apart is measured with a theodolite 
from the other station. 

Then if 26 is the angle subtended by a length 2s, the distance 
is s tan 6. 

This is the method generally employed on long rays. The 
marks are poles set up perhaps fifty feet apart, and the angles 
are measured by the method of repetition. The method has 
often been used on boundary surveys. 

Over shorter rays it is possible to invert the process, and 
instead of measuring the angle which is subtended by a definite 
distance, one measures the distance included in a fixed angle. 
Wires or marks at fixed distances are inserted in the field of the 
theodolite or level, and a graduated staff like a levelling staff" is 
observed. The further away the staff, the greater is the length 
of it included in a fixed angle of sight. The fixed marks in the 
telescope, called stadia marks, are standardised so that one has 
the factor, frequently 100, by which one multiplies the length 
read on the staff to obtain the distance of the staff from the 
observer. 

The factor evidently varies with the distance of the stadia 
marks from the optical centre of the objective of the telescope, 
which is changed in bringing to focus objects at various 
distances. It is not hard to prove that the necessary correction 
for this can be obtained by the simple process of adding, to the 
distance computed as above, the distance from the centre of 
H. M. s. 9 



I30 COMPASS AND PLANE TABLE SKETCHLNG 

motion of the instrument to a point on the axis, outside the 
objective, at a distance from the optical centre equal to the focal 
length. Thus there is a small and slightly variable correction 
to be added to the observed distance to obtain the correct 
result. 

This is not difficult to do ; but the necessity for doing it can 
be avoided by introducing into the telescope a third lens, called 
the anallatic lens, which eliminates the small correction just 
described, and gives at once the true distance from the centre of 
motion of the instrument. A theodolite or level fitted with this 
device is called a tacheometer. The instrument is more useful 
in making detailed plans of a small area than in geographical 
work. 

Correction for slope. 

There is often some confusion as to the correction required 
when the ray is observed on a slope. Without going into the 
proofs, which are quite simple, we may state the rules shortly as 
follows : 

When the subtended angle is measured on the horizontal 
circle of the theodolite, no correction for slope is required. 

When stadia lines or tacheometer are used with a graduated 
bar placed horizontal, the apparent distance must be multiplied 
by the cosine of the slope to give the horizontal distance. 

When the graduated bar is placed vertical, the apparent 
distance must be multiplied by the square of the cosine of the 
slope. 

Summary of exploratory methods of survey. 

It will be useful to sum up briefly the methods which we 
have been considering, suitable for preliminary mapping, ex- 
ploration, or reconnaissance. 

A single-handed traveller, whose main business it is to get 
through the country, on exploration or on official duty, cannot 
make a map. But he can 

(i) make a compass traverse of his route, and fill in a 
small amount of detail on each side ; 



COMPASS AND PLANE TABLE SKETCHING 131 

(2) make astronomical determinations of latitude and 
azimuth, and with much more difficulty of longitude, which fix 
the main points of his traverse, and serve as a general check 
upon it. 

(3) Small areas of country can be sketched with the 
compass and clinometer. 

(4) Larger areas can be mapped by graphical plane 
tabling. 

A traveller like Dr Sven Hedin, who makes long journeys 
alone in Central Asia, relies on methods i and 2. 

Soldiers on active service, who want to illustrate a report on 
the dispositions they have made in a certain position, may use 
method 3- 

A small party of surveyors, sent into unmapped country to 
make a rapid exploration and map, will use method 4, supported 
if possible by 2. 

The most successful explorer will be the man who knows 
precisely the advantages and possibilities of all the methods, and 
makes skilful use of any or all of them as circumstances may 
dictate. 



9—2 



CHAPTER VI 

TOPOGRAPHICAL SURVEY 

Regular topographical survey. 

In the preceding chapters we have considered the various 
operations of survey which may, and should, form part of the 
work of any explorer, or of any pioneer in the development of a 
new country. 

Such work is of the utmost value in the early stages of the 
development of the country. But the time soon comes when a 
systematic survey of the whole must be undertaken. 

No compilation of patchwork survey can produce a map 
worthy of the name, and the sooner the survey of the country is 
put upon a systematic footing, the greater will be the ultimate 
saving of expense, because the less scattered and incomplete 
survey will there be to scrap. 

Preliminary considerations. 

Before laying out the plan of our operations we must con- 
sider whether our aim is restricted to producing a map which 
shall have no sensible error anywhere ; or whether we desire 
that our operations shall be of the refinement required when 
they are to make a contribution to geodesy, properly so called : 
that is to say, to the determination of the size and shape of the 
Earth. 

For the present we will deal with the former case, and 
suppose that we are to undertake the topographical survey of a 
large isolated island, of area about 10,000 square miles. The 
work is to be good, but not of geodetic accuracy. The methods 



TOPOGRAPHICAL SURVEY 133 

employed are to be as economical as is consistent with the 
production of a first-rate topographical map. The island is 
mountainous and the country fairly open, so that it does not 
present any difficulties of an exceptional nature. It is suitable 
for a good theodolite triangulation, with plane table detail. 

The operations divide themselves into the following sections: 

1. Determination of mean sea level. 

2. Preliminary plane table reconnaissance. 

3. Beaconing for the triangulation. 

4. Determination of a latitude, longitude, and azimuth. 

5. Measurement of the bases. 

6. The theodolite triangulation. 

7. Determination of heights by theodolite. 

8. Calculation of the triangulation and heights. 

9. Transference of the triangulation points to the plane 
table sheets. 

10. Mapping by plane table. 

Determination of mean sea level. 

The zero point for heights must be the mean level of the sea 
on the coasts of the island. This must be determined at one or 
more points by the maintenance of tide gauges. 

The tide gauge consists essentially of a well, connected with 
the open sea by a pipe of small diameter, allowing the water in 
the well to assume the average level of the open sea, but damping 
down the quick oscillations of the waves. A float in the well is 
connected with an indicator and scale, so that the height of the 
water in the well can be read at intervals ; or better, it is con- 
nected with a pen drawing a trace upon a clock-driven drum, 
giving a continuous record which can be measured up and the 
results tabulated. 

The selection of a site for the tide gauge is often a matter of 
some difficulty. We require the height of the open sea, and not 
the height of the water in some inlet or harbour, which is often 
modified by prevailing winds and currents. We require that 
the record shall be continuous over a long time, not interrupted 
by choking of the pipe with sand or weed. 



134 TOPOGRAPHICAL SURVEY 

The observed oscillation of the tide is the sum of a great 
number of oscillations of very different periods and amplitudes, 
the shortest periods being the halves of the solar and the lunar 
days, the longest the period of revolution of the Moon's nodes, 
nineteen years. 

Further, variations of the barometer affect the height of the 
sea, a fall of the barometer by one inch being accompanied by a 
rise in the sea of about one foot. 

Hence it is not possible to lay down any definite period 
during which tidal observations should be continued. Fifteen 
days' observation will cover the principal lunar tides, and this 
may be taken as the absolute minimum. The best procedure 
is to set up the tide gauge as early as possible, and to prolong 
the observations as long as possible. 

For the ordinary purposes of topographical mapping one 
station is enough. But if it is proposed to carry out precise 
levelling, and especially if there is any chance that questions of 
rising or tilt of the land will arise, then several tide stations will 
be required. In the present chapter we shall be content with 
one station. 

It is essential that the tide gauge shall be set up on solid 
ground, so that there shall be no question of the permanence ot 
the zero of the scale. It has usually happened that the longest 
series of tidal observations have been made at ports ; but the 
value of these series has been much depreciated by the fact that 
ports are very often on made ground, with no guarantee against 
gradual settlement. Sometimes indeed it is found that the 
whole ground itself rises and falls with the tide. 

The zero of the tide gauge must be connected with one point 
of the triangulation by a carefully observed line of levels, (See 
pages 95, 187.) 

A discussion of the instrumental details of tide gauges, or of 
the manner of reducing tidal observations, is entirely outside the 
scope of this book. Reference may be made to the Publications 
of the Survey of India, the Handbooks of this Survey, and 
to Sir George Darwin's work. The Tides. 



TOPOGRAPHICAL SURVEY 135 

The plane table reconnaissance. 

The success of the whole operation depends upon obtaining 
a good triangulation ; and the difference between a good and 
a bad triangulation depends largely upon the efficiency of the 
reconnaissance which must precede the choice of the stations. 

It is surprising how many small impediments combine to 
interrupt the mutual visibility of stations that might be expected 
to be in full view of one another. Hence it is not safe to take 
for granted the most seemingly obvious suitability of any 
particular station. A plane table reconnaissance starts without 
taking much trouble over the measurement of a base, for the 
precise scale of the sketch is immaterial. Rays are drawn to 
three or four times as many points as are likely to be wanted, 
for it is certain that as the work proceeds it will be necessary to 
drop many of the points for obstruction on one ray or another. 
At the conclusion of the reconnaissance the surviving points 
will be carefully studied, from the point of view of planning a 
well-conditioned system of triangles, and of obtaining a good 
connection with the measured bases. 

During the preliminary reconnaissance the ground should be 
beaconed, and care should be taken that not only the general 
localities are intervisible but the beacons themselves. Want of 
care in this respect may cause endless trouble afterwards, for the 
actual triangulation with the theodolite is a slow and laborious 
business, and the failure of a single station means that a number 
of other stations must be re-occupied. Hence no pains may be 
spared in making sure that every ray in the selected arrange- 
ment is really observable. 

It is hardly necessary to say that the most anxious attention 
must be given to the selection of sites for the bases. 

The reconnaissance ladder. 

In suitable country the plane table triangulation is easy. 
But it may be required to cross a low and forest-clad district 
where it will be necessary to build towers for the instrument, 
and the selection of the sites for these towers is difficult, because 
until they or their equivalents are erected it is impossible to 
judge of the suitability of their positions. To get over this 



136 TOPOGRAPHICAL SURVEY 

difificulty a French officer of Artillery, Commandant Lucien 
Durand, has introduced into survey the tall observation ladder 
that is used for the control of artillery in modern practice. This 
ladder can be carried on a waggon and run up in an hour. 
From the opening in the platform at the top the surveyor can 
work his plane table, and can decide very well whether or not 
the position is suitable for the erection of a tower station. The 
same officer has designed a very steady construction of poles 
which makes an excellent and inexpensive tower. (See 
Plate XVII.) 

Plan of the triangulation. 

It is not necessary that the principal triangulation should 
cover the whole country with a net of triangles. If the country 
is long and narrow a backbone of quadrilaterals is sufficient, as 
in the figure. If the breadth is too great to make this sufficient, 
a chain of quadrilaterals at right angles to the first will strengthen 
the skeleton. 

The purpose of forming the triangles into chains of quadri- 
laterals is to provide the necessary control without unnecessary 
repetition or duplication. Were the chain a chain of triangles 
only, there would be no check upon the survival of a gross error. 
A regular system of quadrilaterals gives the most simple 
arrangement consistent with strength. 

It will often happen that more rays can be observed from a 
certain station than are required by the plan. To observe these 
rays would confuse the work without adding anything of im.- 
portance to its accuracy. Hence the desirability of making a 
strict programme of the rays to be observed at each station, 
neglecting all others. 

The triangles must be well conditioned : that is to say, they 
must be strong in shape, having no angles less than 30^ about, 
and if possible none less than 40°. The size of the triangles will 
depend so much on the nature of the country that no general 
rule can be laid down, beyond saying that the larger they are 
the better. 

The connection of the bases with the chains of quadrilaterals 
also depends very much on the ground. The main idea is that 



Plate XVII 




I. Reconnaissance ladder on the march. 



^-^iO-*- 





Reconnaissance ladder in 
course of erection. 



3. Double tripod scaffold for 
theodolite and observer. 



fieconnaissance ladder and beacon. 
Service Geographique de VArniee. 



Designed by Commandant L. Ditrand, 
11" Rcpinient d'Ariillerie. 



TOPOGRAPHICAL SURVEY 137 

a chain should start from one base and close on another. Then 
the comparison between the length of the second calculated 
through from the first and the length of the second as actually 
measured gives the best possible control over the accuracy of 
the whole chain. 




Fig. 18. Diagram of Geodetic Triangulation up the Nile Valley from Cairo 
to Beba. The two heavy lines are bases. 

Beacons. 

Beacons are of two principal kinds : the luminous and the 
opaque. In most countries, when the ray is more than eight or 
nine miles long it is necessary to use luminous beacons or 



138 TOPOGRAPHICAL SURVEY 

signals, for the haze in the air very quickly obliterates the 
contrast between the opaque signal and its surroundings, so that 
it becomes invisible. 

Luminous signals are either heliographs, for use with the Sun 
by day ; or powerful lamps, nowadays usually acetylene, for 
work at night. In a fine climate like South Africa, the 'helio' 
can be observed at a range of lOO miles and sunlight is sufficient 
to let the work proceed without undue delay. In less favourable 
climates lamps provide a more certain mark for observation ; 
but there may be difficulties in observing at night, for reasons of 
health or safety, that make it necessary to restrict operations 
to the day. On cloudy days it is sometimes possible to use 
powerful lamps instead of helios. Night observation has the 
great advantage that irregular refraction and disturbance of the 
air are much less than by day, so that the results are more 
accurate. 

In either case, the effective use of luminous signals requires 
that the organisation and control of the signal parties shall be of 
a high order. Each party must use every endeavour to send its 
signal in the right direction so long as it is required, and must 
then move without delay to the next station. In general the 
discipline must be military to ensure the punctual carrying out 
of the lonely, dull, but all-important duties of the helio or lamp 
parties. 

The heliograph. 

It is impossible to enter into details of the mechanical con- 
struction of this instrument. Essentially it is a plane mirror 
from three to eight inches in diameter, mounted on a tripod in 
such a v/ay that it may be turned by means of a slow motion 
screw to follow the Sun, and cast the reflected beam in a constant 
direction. There is a sight vane carried on an arm, which is set 
in the first instance upon the station to which the beam is to be 
directed ; and a small round patch is left unsilvered in the 
centre of the mirror. So long as the black spot thus formed in 
the beam is kept centred on the white patch of the sight vane, 
the beam is being sent in the right direction. 

It is sometimes a matter for surprise that the beam can be 



TOPOGRAPHICAL SURVEY 139 

directed with the necessary accuracy, until one remembers that 
the Sun, and therefore the beam, has a diameter of half a degree. 
The light from the mirror therefore diverges in a cone of angle 
half a degree, equivalent to about i in 115. At a distance of 
ten miles the beam covers a front of about 150 yards, and a 
careful operator has no difficulty in directing the beam within 
this distance right or left of the object. 

When lamps are used, at night, the distant station is invisible, 
and some means must be devised for sending the beam in the 
right direction. But it is hardly possible to go into such detail 
in this place. 

It is interesting to remember that the limelight was invented 
by an officer of the Royal Engineers to make the connection 
between Wales and Ireland, after many weeks had been wasted 
in waiting for the Sun. 

Opaque signals. 

The opaque signals must be large, so that they may be 
visible at a distance ; and they are best constructed so that 
the theodolite may be placed in position without taking down 
the signal ; otherwise there is some danger that the signal will 
not be re-erected in its original position, and there will be a dis- 
continuity between the observations made to that station before 
and after its occupation. 

The construction of the beacons will vary with the materials 
locally available and with the ease or otherwise of transport. 
They should be symmetrical about their vertical axis when seen 
from any position ; therefore the quadripod is preferable to the 
tripod. A good form of signal is that shown in the frontispiece 
to Colonial Survey Reports, Vol. 2. Its appearance on service is 
shown by the accompanying photograph of a beacon on the 
Uganda-Congo boundary, for which I am indebted to Captain 
Jack, R.E., British Commissioner. (See Plate XVIII.) 

In unsettled countries the surveyor has the advantage that 
he can cut down trees to make his signals ; an official manual 
recommends a form of beacon built of 120 saplings. He can 



140 TOPOGRAPHICAL SURVEY 

also clear the tops of hills of inconvenient timber, leaving the 
best tree standing in which to build a station. In civilised and 
closely settled countries this is not possible ; but church towers 
and other buildings go far to supply the need. The Ordnance 
Survey of England constructed a station above the cross on the 
dome of Saint Paul's, and took off temporarily some feet of the 
top of the spire of Norwich Cathedral. Such operations being 
impracticable under ordinary circumstances, it is very difficult to 
carry out a piece of triangulation in England for instructional 
purposes on any considerable scale. 

Permanent marks underground. 

In all cases the visible signal should be considered as a 
temporary representation of an underground mark, which is 
buried for safety, and so protected and identified that it may be 
recovered at any time. To ensure this is not easy. Some of 
the principal stations of the Ordnance Survey of England are 
now lost, owing to insufficient attention to this question of 
permanent marking. 

The form of the underground mark depends on local circum- 
stances. It will take some such form as a copper bolt let into 
the rock at a depth of say two feet, and protected by a pyramid 
of masonry, or a large cairn of stones. In settled countries a 
few square yards of ground should be bought and enclosed ; it 
may then be committed to the charge of the local authorities. 
In unsettled countries it is much more difficult to protect the 
stations, because the natural tendency of the native is to take 
the first opportunity of digging to see what it is that the white 
man has buried so carefully. In these countries also great 
trouble is often experienced in maintaining the opaque signals, 
and much time is wasted through their destruction during the 
course of the work. 

Self-centering beacons. 

With the usual construction of beacons a great part of the 
time taken in setting up the instrument is consumed in centering 
it over the station mark. And a considerable part of the gradual 
loss of accuracy in the progress of the chain of triangles is 



Plate XVIII 




I. Heacon for interscrtccl point. 





2. Quadripod beacon for tnanyulalion. 
gcmda- Congo Boundary. Phot. by Capt. E. M. Jack, R.E. 



TOPOGRAPHICAL SURVEY 141 

caused by errors in this setting up and centering. To avoid 
these difficulties an excellent form of self-centering beacon has 
been introduced by the Survey of Egypt. The beacon consists 
of a concrete pillar carrying on top a brass casting with three 
radial V-shaped grooves planed at 120° apart. The three 
levelling screws of the theodolite base, or the three feet of the 
helio, stand in these grooves. The instrument can be put up 
only in one position, which is automatically the correct one, and 
no error of centering is possible. When the station is not in use 
the pillar is covered over and protected. in the usual way. This 
self-centering device seems to be worthy of general adoption. 

Beaconing. 

The selection of sites for the beacons is done by a 
reconnaissance party making a plane table sketch well ahead 
of triangulation party, and erecting the beacons on the points 
which make the best conditioned system of triangles. The 
beaconing party is responsible for leaving everything in order 
for the triangulators ; and they must take great care that all the 
rays are cleared and fully visible. 

Initial latitude, longitude, and azimuth. 

The triangulation and plane tabling will eventually produce 
a map in which all parts of the ground are shown in their 
correct relation one to another; but they will give no information 
as to the place of that country on the Earth. To fix the map 
down on the Earth, and to obtain its orientation, we must make 
astronomical observations. 

By determining the latitude and longitude of one of the 
triangulation points we, so to speak, pin the map down at one 
point, leaving it free to turn about that point. By determining 
the azimuth of one of the rays from this point to any other, we 
fix the map in its right orientation. 

Hence the necessary astronomical observations are 
An initial latitude and longitude. 
An initial azimuth. 

It might be supposed that there would be some advantage in 
determining the latitudes and longitudes of a number of different 



142 TOPOGRAPHICAL SURVEY 

points. But for our present purpose this is not so. The reason 
will be discussed more fully in the chapter on the astronomical 
observations for geodetic purposes. For the time being it will 
be sufficient to say that every observed latitude and longitude is 
affected by local irregularities in the direction of gravity, due 
to the unequal distribution of mass in the crust of the Earth. 
Hence if one observes the latitudes of two stations in the 
triangulation one will probably find that the difference of the 
observed latitudes does not correspond with the difference of 
latitude resulting from the triangulation. Such discordances are 
of the highest importance in geodesy. But in a simple topo- 
graphical survey they are embarrassing ; and it is usually best 
to confine oneself to a single latitude and longitude ; and a 
single azimuth. 

Observation of latitude. 

The determination of latitude will be made by the observa- 
tion of stars near the meridian : the method of circum-meridian 
altitudes. Observations of the stars are always to be preferred 
to observations of the Sun, both because they are more accurate 
in themselves, and because a number of stars can be observed 
on one night, so that a determination of the accuracy desired 
can be obtained very much more quickly than if the Sun were 
used. 

Two or three nights' observation with a five-inch micrometer 
theodolite taking four pairs of north and south stars each night, 
should give the latitude correct to one or two seconds of arc, 
which is less than the probable value of the local deviation of 
gravity, and is sufficient for all topographical purposes. 

Should a more elaborate determination of the latitude be 
desired, it will be obtained with the zenith telescope, or with a 
large theodolite constructed to serve as a zenith telescope. 

Observation of longitude. 

The longitude of the initial station is the difference between 
its local time and the time of the meridian of Greenwich. 

The local time at the initial station will be determined by the 
observation with the theodolite of pairs of stars east and west, as 



TOPOGRAPHICAL SURVEY 143: 

near the prime vertical as possible. Or, more elaborately, it will 
be determined by a portable transit instrument set up at the 
initial station. 

The difficulty, as always, lies in obtaining the time of the 
Greenwich meridian. With the extension of wireless telegraphy 
this difficulty becomes less year by year, and will shortly dis- 
appear. It is therefore not necessary to discuss the difficult and 
now out of date methods of obtaining Greenwich time indepen- 
dently of the telegraph or wireless. By the use of wireless it. 
becomes relatively easy to determine longitude well within a 
second of time. When it becomes a question of one or two 
tenths of a second all kinds of complications arise, which need 
not be discussed here. (But see Chapter VIII, page 198.) 

Observation of azimuth. 

The azimuth is obtained by observation of stars east and 
west, near the prime vertical, or of circumpolar stars at their 
greatest elongations. These observations give the difference of 
azimuth between the stars and the terrestrial station, and also 
the true azimuths of the stars at the moments of comparison ; 
whence the true azimuths of the station are immediately derived. 

If the triangulation is being made with opaque signals, so 
that no provision is made for illuminating the signals at night, it 
will generally be convenient to establish a supplementary mark 
at a moderate distance, say one mile, from the initial station. 
This mark can be more easily illuminated than one at a greater 
distance; and the difference of azimuth between the mark and 
the triangulation station chosen for the initial azimuth can be 
determined during the ordinary course of the triangulation by 
day. 

There will be no difficulty in determining the initial azimuth 
in this way with an accuracy of two or three seconds of arc, 
which is sufficient for the purposes of the survey with which we 
are dealing at present. Local deviations of gravity have their 
effect on azimuths as well as on latitudes and longitudes; and it 
is useless to aim at a degree of accuracy which cannot be achieved 
except by the elaborate discussions of geodesy. 



144 TOPOGRAPHICAL SURVEY 

The bases. 

Recent improvements in the means of measuring bases have 
altered our conception of the relation of the base to the triang-u- 
lation. When base measurement was difificult one thought of the 
triangulation as built upon a single base, whose measurement 
was by far the most delicate, the most anxious, and the most 
uncertain part of the whole operation. If it were possible to 
measure a second base in another part of the country, well and 
good. But it would never have been thought remarkable if a 
whole survey rested upon one base. 

Nowadays base measurement has become so relatively easy 
that it is possible to plan a chain of triangulation and to stipulate 
that bases shall be measured at intervals of 200 or even 100 
miles apart all along the chain. The measurement of a base 
becomes a kind of control carried out at intervals as part of the 
routine ; it is no longer the solemn and fundamental operation 
that it was. 

Essentials of base measurement. 

The essential steps in the process of base measurement are 
the following : 

1. Determination of the field standard in terms of the 
national standard of length. 

2. Measurement of the distance between the base terminals 
on the ground in terms of the field standard. 

3. Correction of the measure for temperature and any other 
causes of variation, and reduction to national standard. 

4. Reduction to the horizontal, and then to mean sea level. 

For topographical purposes bases may be measured by means 
of tapes laid along a straight and level road or raihvay track, 
and stretched to a constant tension with a spring balance; or by 
a wire or tape hung under constant tension in the natural curve 
— the catenary — supported at each end by frictionless pulleys 
suspended from trestles, and carrying near each end a divided 
scale which is read against marks carried on tripods set up along 
the line of the base. 



TOPOGRAPHICAL SURVEY 145 

The tape laid on the ground serves very well when there is a 
convenient railway track with little traffic, such as is often avail- 
able in large and new countries. In the absence of such ready- 
made sites for the base, it is easier to use the wires hung on 
tripods some feet above the ground. Much rougher country can 
be crossed, and it is easier to go up and down hill. We shall 
consider the latter method as the standard modern method, and 
shall deal with it first. 

The tape or wire. 

The modern tape or wire is either 100 feet or else 24 metres 
long between the divided scales. It is made of an alloy of nickel 
and steel (36^ nickel) which has the remarkable property that 
its coefficient of expansion is only one tenth that of ordinary 
steel, "000,000,5 of its length per degree Fahrenheit, instead of 
•000,006. The trade name of this alloy is Invar. 

These tapes or wires have the great advantage that they are 
extremely portable. When wound upon their reels they may be 
sent by post to the National Physical Laboratory or to the 
Bureau International des Poids et Mesnres at Breteuil, and there 
compared with the laboratory copies of the national standards 
of length. For a comparatively small fee the laboratory will 
determine the correction to the assumed length, and make a 
determination of the coefficient of expansion with temperature. 
Thus without any difficulty a survey department in, we will say, 
Fiji, may send home the standard tapes from time to time to be 
re-compared with the laboratory standards, and may thus ensure 
a very strict control over the lengths of the wires or tapes that 
are in actual use in the field. 

This provides in a very simple and inexpensive way for the 
reference to the national standards of length. 

Use of the suspended tape in the field. 

The base will be from four to twelve miles long : the longer 
the better. It must be chosen so that one end is visible from 
the other ; and it is generally convenient that the ends shall 
be on slight elevations, which much facilitates the choice of 
the stations for the base extension, that is to say, of the small 
H. M. s. 10 



146 TOPOGRAPHICAL SURVEY 

triangulation connecting the base with one of the principal sides 
of the main triangulation. 

The ends of the base will be marked by terminals sunk in 
the ground, or perhaps carried on concrete pillars. 

Simple but firm tripods, carrying small upright pillars 
engraved with fine lines, will be set out in the line of the base, 
at distances apart equal to the tape length between its zeros of 
the engraved scales. 

The tape is suspended over frictionless pulleys, carried on 
straining trestles which can be adjusted easily so that the tape 
can be brought up close to the marks on the tripods. The tape 
is kept in tension by weights hung on each end. 

At given signals observers at each end make series of 
simultaneous readings of the scale on the tape, against the 
marks on the tripod. 

The tape is then carried on to the next tripod section, and 
the operation is repeated. 

As soon as the tape party is clear a levelling party determine 
the difference of height between one tripod and the next. When 
this is done, the tripods in rear can be carried forward and set 
up ahead in the line of the base. With good organisation and 
drill it is possible to measure five kilometres per day in this 
manner. 

At the beginning and end of each day's work the field tapes 
are compared with the tapes which have been standardised in 
the laboratory, and which are not subjected to the risks of injury 
in the field. 

The accuracy obtainable in this way is limited only by the 
number of wires which are employed, the number of times that 
the measures are repeated, the precautions that are taken to 
avoid damage to the wires, and finally, by the residual error in 
the comparison of the standard tapes with the laboratory 
standards of length. 

With very little precaution it is possible to measure topo- 
graphical bases in this way with an accuracy of i in 200,000, 
which is amply sufficient for any work which does not aim at 
geodetic accuracy. We shall consider the refinements desirable 
in the measure of geodetic bases in a separate chapter. 



Plate XIX 




I. Taking readings on the wire, Semliki Base. 




Adjusting the straining trestle and wire before reading. 

Phot, by Capt. E. M. Jack, R.E. 



Measurement of Semliki Base, 
Uganda- Congo Boundary. 



TOPOGRAPHICAL SURVEY 147 

Use of the flat tape in the field. 

The tape laid on the ground will probably soon become 
obsolete, except for operations on a small scale. 

A convenient way of operating with such a tape is as 
follows : 

Provide the tape with two handles filed flat at their ex- 
tremities. The distance between these extreme surfaces is the 
length of the tape which is compared with the standard. The 
handles are furnished with lugs, over which are hooked wire 
stirrups with a loop at the end, to take the hook of a spring 
balance. 

Pickets are driven into the ground in the line of the base, at 
tape lengths apart, and strips of zinc are nailed to the tops of 
the pickets. The tape is held at one end by a spike through 
the loop of the stirrup, and is strained to the right tension by a 
spring balance hooked into the other stirrup. The flat ends of 
the handles should then come over the zinc strips. At a given 
signal observers at either end steady the tape, and draw a sharp 
point along the flat ends of the handles, so as to make marks on 
the zinc strips. The tape is then carried on to the next section, 
and the operation repeated. No attempt is made to join up the 
tape lengths accurately, but the distances between the pairs of 
cuts on the zinc are measured with scales or dividers, and the 
small excesses or defects added to the tape lengths. The 
thermometer is laid alongside the tape on the ground, and is 
read at frequent intervals to give the temperature correction. 

Working in this way it is easily possible to measure a base 
with an accuracy of i in 75000, provided that a good site can 
be secured. But unless a straight railway track is available the 
suspended tape is easier to manage though it requires a larger 
party. 

For details of the use of tapes laid flat on the ground refer- 
ence may be made to Wilson's Topographical Surveying. 

Correction for slope. 

With modern ideas of ground suitable for base measurement, 
the correction for slope sometimes becomes considerable ; but it 
is always very simple. 



148 TOPOGRAPHICAL SURVEY 

The correction may be expressed in terms of either the 
vertical difference in height of the ends of the tape, or the slope 
of the straight line joining the ends. 

Considered in its simplest possible form the problem is as 
follows : 

Let L be the length of the tape, or the distance between the 
zeros at the two ends; and let H be the difference in height of 
the two ends. If ^ be the slope of the tape, then sin 6 = HjL ; 

and the correction for slope is — L{i — cos 0)=^ — H'^\2L. 

Hence, whether the slope or the difference of vertical height 
is measured, the correction to the measured length of each span 
is very simple. Modern practice favours the use of the differ- 
ences of vertical height, measured with an ordinary Y-level, 
rather than slopes measured with an instrument such as the 
Abney level. 

It may seem to be likely that the above simple assumption 
as to the form of the correction is not applicable to the case of a 
tape hanging in its natural curve. An exact investigation shows^ 
however, that except in the most minutely refined work, the 
above formula is amply accurate. (See page 187^ 

Reduction to sea level. 

It is an invariable principle that maps should be drawn as if 
the ground were projected on the sea level surface. A moment's 
consideration shows that this is necessary. Think of two parallels 
of latitude crossing the Drakensberg from Natal to the Orange 
Free State. The ground on the latter side is nearly a mile 
further from the centre of the Earth than the low land in NataL 
Hence the linear distance between the parallels will be greater 
by about one part in four thousand on the west side of the 
range. But it would be quite impossible to represent the 
difference on the map, since such a representation would require 
that the sheet should be stretched locally wherever the ground 
was high. Hence the necessity of reducing always to sea level. 

The reduction is of great simplicity, being almost automatic 
in its operation. Let h be the mean height of the base above 



TOPOGRAPHICAL SURVEY 149 

sea level, and R the radius of the Earth, supposed spherical. 
Then the simple reduction of the measured length L of the base 
is evidently — LhjR very nearly. This is quite sufficient except 
in extremely accurate geodetic work ; the latter we will consider 
in a later chapter. 

With our base thus reduced to sea level the calculation of 
the whole triangulation, depending on the base, is automatically 
reduced to sea level also, as we shall see almost immediately. 

The theodolite triangulation. 

The theodolite is set up directly over the station mark, and 
is levelled, so that the horizontal circle of the instrument is truly 
horizontal. The telescope is sighted on each of the other stations 
in turn, according to the programme ; and the horizontal circle 
is read by the microscopes at each setting. It is important to 
notice that the angles thus measured are not the actual angles 
between the successive pairs of beacons, such as would be 
measured by a sextant, but are those angles projected on to the 
horizontal plane of the station occupied. If the Earth is con- 
sidered spherical these angles are the same whatever the height 
of the stations above sea level, even when the various stations 
are at very different heights. Hence the justification for the 
statement of the preceding section, that when the measured 
base is reduced to sea level the whole of the triangulation is 
automatically reduced to sea level also. 

The details of the manipulation of the theodolite are dealt 
with in the Textbook of Topographical Surveying. We will 
confine ourselves here to the points which are especially con- 
cerned with the horizontal triangulation. 

Suppose that there are four stations A, B, C, and D to be 
observed. A round of angles consists of settings on A, B, C, D, 
and A in turn. It is important to notice that the station A is 
observed to twice. The reason for this is that small errors are 
introduced into the measured angles if the instrument is not 
perfectly stable during the course of the round ; and this cannot 
be ensured absolutely. If we repeat the observation o{ A at the 
end of the round we ensure that the measure of the angle DO A 
is independent of any settlement of the instrument that may 



ISO 



TOPOGRAPHICAL SURVEY 



have occurred during the course of the round from A to D. In 
fact any such movement affects only the particular angle under 
measurement at the time when it occurred. At the same time 




Fig. 19. 

the near concordance that there should be between the first and 
the last settings on ^ is a measure of the stability of the instru- 
ment during the round. This is an important principle, to which 
attention should be paid. 



There are, however, cases in which the simple process 
described above must be modified. In a bad climate it will 
happen that sometimes one and sometimes another station is 
visible ; but never all at once. In such a case one establishes a 
reference mark at such a distance that it is always visible ; and 
one measures the angle between this mark and any other station 
that may become visible. The differences between the bearings 
of all the stations from this reference mark give eventually the 
angles that should have been observed directly. For simplicity 
we shall assume in what follows that the whole round of angles 
can be observed in the manner first described. 

To obtain the necessary control and to detect blunders, as 
well as to eliminate by repetition the accidental errors of the 
observations, the round of angles must be repeated one or more 
times. We take care to arrange the work so that each repetition 



Plate XX 



.-s^^ 





I. In position for Triangulation. 



2. From the eyepiece end. 





3. With reflector over objective for 
lamp illumination. 



4. With attachment for 
electric illumination. 



Five inch Mic7-oinete7- Theodolite. 



Cambi'idge Observatory. 



TOPOGRAPHICAL SURVEY 151 

is made on a different part of the circle, whereby accidental errors 
of the circle graduation are to some extent eliminated. In the 
very best instruments these errors rarely exceed two or three 
seconds of arc ; but there are many instruments in use, made by 
well-known makers, in which the errors of graduation are by no 
means so sm.all. It would be a very long and tedious business 
to determine them and introduce corrections for them ; and it is 
usually sufficient to so arrange the observations that repetition 
tends to eliminate them. 

Check on the accuracy of the triangulation. Triangular 
error. 

In a small triangle, of one or two miles per side, the curvature 
of the Earth may be considered negligible, and the three angles 
of the observed triangle should add up to 180°. In larger 
triangles this is not strictly the case. We remember that the 
angles are measured in the horizontal planes through each 
station ; and when the triangle is large the curvature of the 
Earth throws these planes out of parallelism with one another. 
The result of this is that the three angles of the triangle should 
add up to more than 180°, the excess being called the 'spherical 
excess.' This is easily calculated, and depends on the area of 
the triangle. Deduct it from the observed sum of the three 
angles, and the result should be 180° exactly. In practice it 
will differ from this quantity by a small number of seconds, 
and this difference is called the ' triangular error.' 

The average triangular error is a measure of the precision 
of the triangulation. In the most precise work, of geodetic 
accuracy, the average error will be less than one second of arc. 
In good topographical triangulation it will be two or three 
seconds. Experience will show what limit should be set to the 
average triangular error on any particular piece of work ; and 
when the standard is laid down the observations must be repeated 
as many times as may be necessary to arrive at the desired 
degree of accuracy. 

This test of the triangulation by considering the triangular 
error gives a simple and invaluable means of control, and of 
securing that the work is up to the standard required. 



152 TOPOGRAPHICAL SURVEY 

Spherical excess. 

The spherical excess of a triangle may be calculated from the formula 

„ , ■ ^ cosec i" 
h=ab sm C , — j^. — rs . 
2 (radius)'' 

When the ellipticity of the Earth is taken into account it is usual to work 
with the radius of an oblique section making an angle 45° with the meridian. 
See Auxiliary Tables of the Survey of India, Table III. 

If the triangles are less than 100 miles a side it is sufficiently accurate to 
apply to each angle a correction of one third of the excess. 

Except in very accurate work it is sufificient to measure the area of 
the triangle from a chart, and to use the formula 

„ area of triangle in sq. miles ,, 

E= X 13-15. 

1000 -^ ^ 

Refraction of horizontal angles. 

Refraction is usually supposed to act in a vertical plane ; 
and so long as it does so it can have no sensible effect upon the 
horizontal angles. But in the neighbourhood of steep slopes the 
layers of air of different temperatures are not horizontal, and 
a ray of light passing through such a region may suffer deviation 
in the horizontal plane. Such effects will in general take place 
only near the ground ; and for this reason it is important to 
avoid rays which in their course approach near intervening 
ground. Such rays are called ' grazing rays.' 

It is difficult to say how high a ray must pass over inter- 
vening ground to avoid the disadvantage inherent in a grazing 
ray ; but so long as obviously grazing rays are avoided it is 
usually safe to hope that such small remaining effects of 
horizontal refraction as may be left will be of a non-systematic 
character, and will be eliminated in the average. There are, 
however, certain cases where this is not necessarily true, such as 
in the triangulation up the valley of the Nile, where the stations 
are alternately on opposite cliffs, and the cooling of the air over 
the water might very well produce systematic effects. Much 
attention is being given to this problem by the officers of the 
Survey of Egypt. 



TOPOGRAPHICAL SURVEY 153 

A recent publication of the United States Coast and Geodetic 
Survey, on the Texas-CaHfornia arc of primary triangulation, 
gives a striking instance of well determined lateral refraction. 
The line between two stations Clayton and Kennard passes very 
close to a steep slope of a flat topped hill. During most of the 
observations the wind was blowing from the hill across the line 
between the stations, and the results gave excessive closing 
errors to the triangles involving this line. The observations 
made when the wind was blowing across the line towards the 
hill gave values which closed the line in a satisfactory manner. 
It became evident that the former were in error by about seven 
seconds of arc. 

Determination of heights by theodolite, or Trigono- 
metrical Heights. 

The method of trigonometrical heights provides a rapid way 
of determining differences of height of the triangulation points. 

During the occupation of each station, after the horizontal 
angles have been measured, the apparent angular elevation of 
the beacons at the other stations are measured with the vertical 
circle and microscopes of the theodolite. These measures differ 
from the horizontal angles in that they are absolute elevations 
or depressions, and not merely differential measures. 

By careful attention to the rules for the measurement of 
vertical angles the errors of the instrument may be very nearly 
eliminated, except that there is no possibility of eliminating the 
errors of division of the circle by repetition on different parts of 
the arc. The serious errors inherent in this method are those 
due to refraction. 

The vertical refraction of a horizontal ray is large; it depends 
upon the density of the air intervening in the path of the ray, 
which varies very rapidly during the day, and is almost im- 
possible to calculate. But there are two principles of working 
by which this effect may be in great part avoided : the observa- 
tions should be made at the time of day when the refraction is a 
minimum, that is to say, in the early afternoon ; and the rays 
should be observed from opposite ends under circumstances as 
nearly the same as possible. It is then assumed that the effect 



154 



TOPOGRAPHICAL SURVEY 



of refraction on the observation at each end is the same ; and it 
is easy to see that the effect is thereby eliminated. 

When it is not possible to take the reciprocal observations 
from each end, some assumption must be made as to the law of 
refraction, based upon an analysis of the observations that have 
been made reciprocally. But to pursue this part of the subject 
is beyond the scope of the present chapter. The results are 
especially unsatisfactory in mountainous regions with glaciers 
and perpetual snow. Hence the heights of the inaccessible 
snow-clad peaks of the Himalayas, which are determined by this 
method, are subject to some uncertainty. 

It will be noticed that when two points at a considerable 
distance apart, and of no great difference of height above sea, 
are reciprocally observed, each is measured as a depression at 





Fig. 20. 



Fig. 21. 



the other, in spite of the fact that refraction raises each of the 
rays to some extent. This is a necessary consequence of the 
curvature of the Earth ; but the size of the effect is a little 
surprising to the student, until he remembers how small the 
Earth really is, and that two points four geographical miles 
apart subtend an angle of four minutes of arc at the centre of 
the Earth, so that each is depressed from the other by 2'. 

The formulae are very simple. 

Let A, B be the two stations, and AI a point vertical!)' below B at the 
same distance from the centre of the Earth as A. 

Since AB \s very small compared with AC, we may take 

BjW= AM tsin BAM. (Fig. 21.) 



TOPOGRAPHICAL SURVEY 155 

And it is easily seen that BAM is equal to half the difference in the 
depressions of the two stations, seen from one another : provided that the 
refraction is the same at the two ends. 

Hence \i s be .the distance in feet between the two stations, their difference 
of height in feet is staw^ (difference of depressions). 

If only one angle is observed it is necessary to introduce a numerical 
allowance for refraction. Whenever reciprocal observations are obtained, as 
above, the refraction at either station is i? = ^ (5 — sum of observed depressions) 
where 6 is the angle ACB, which can be calculated from s and the radius of 
the Earth. It is found that the ratio B : 6 \s generally about o"07. 

Now it is easily seen that for an observed depression D at B the angle 

BAM=id - refraction - D. 

And if refraction = o'o7 ^ this becomes 

BAM=o-436-B. 

Or since the distance along the surface corresponding to an angle of 
i" at the centre is about loi feet 

^^^j^^ 4"'25 X distance in feet ^ 
1000 

= K — D say. 

And then as before 

difference of height = j- tan (k — Z?). 

This is the simple theory on which the table for k given in the Textbook 
of Topographical Surveying is based. 

The whole of the above theory is a rough approximation ; but it is 
probably sufficient, in view of the uncertain effects of refraction. 

We must also take into account in the calculation the height of the 
theodolite above ground at each station, and also the heights of the signals 
to which the observations are made. It is tedious to puzzle out the rules 
of signs for these small corrections ; but it is quite easy to apply them when 
the rules are given. See Textbook of Topographical Surveyings pp. 28 
et seq. 

When all precautions are taken the errors of this process 
amount to one or two feet on a ray of thirty miles, when the 
angles are observed at each end. For rays observed only from 
one end, and especially when there is a probability of anomalous 
refraction, such as occurs in mountainous regions with glaciers, 
the uncertainty is considerably greater ; but it may of course be 
reduced by combining the results of a number of observations 
taken from different stations. 



IS6 TOPOGRAPHICAL SURVEY 

The heights of most of the principal peaks in the Himalayas 
depend upon rays observed from one end only. Lines of 
levelling have been carried up to stations in the hills, and from 
these trigonometrical heights of all or of many of the 10,000 
permanently snow-clad summits have been observed. During 
the course of such work Mount Everest had been observed to 
on many occasions without any suspicion that its height was 
extreme, for it is very inaccessible, and does not appear 
strikingly prominent compared with other peaks. Only when 
the observations were computed in due course in the Survey 
Department at Calcutta was it found that this peak is higher 
than any other known ; and not until after the Tibet Expedition 
was it certain that there is not a higher peak behind it. 

Barometer heights in topographical survey. 

Although the barometer cannot be relied upon for the 
principal determinations of height in regular survey, it is often 
useful in special circumstances, Avhen the other methods fail. 

For example, suppose that it is necessary to determine 
the depth of a canyon with almost perpendicular walls. Very 
probably the bottom of the canyon cannot be seen from the top, 
and methods depending upon observed rays are useless, or at 
any rate can be employed only at the cost of great trouble 
in occupying many intermediate stations. In such a case a 
barometer trip to the bottom and up again will give results 
which are sufficiently accurate, in a few hours. Similarly the 
barometer may be employed in contouring densely wooded hill 
country, in which no view can be obtained, and which is being 
surveyed by traverse. This method is much used in Nigeria. 

Calculation of the triangulation. 

The obsen-ations made at each station are entered in ' angle books,' from 
which the observed angles are abstracted, the means taken, and the results 
brought together in the form of abstracts of angles.' 

Let the figure represent a part of a chain of quadrilaterals under observa- 
tion. A portion of the abstract of angles may read thus : 
Observed angles at Y : EYD 31° 57' 28" 
DYF 45 6 15 
FYE 282 56 9 

359 59 52 



TOPOGRAPHICAL SURVEY 



157 



It will be noticed that the angles at the station do not add up to precisely 
360° as they should. This is due partly to the errors of observation, partly 
to the errors of the divided circle, and partly to movement of the instrument 
in the course of the round. 

Now suppose that in the course of the computation we have arrived at 
the length of the side DE and that we wish to proceed. Let us do so by 
solving the triangle DE V. From the abstract of angles at V we take out 

EVD 31° 57' 28" 
and from the abstracts of angles at D and E we take out 

VBE 55° 28' 16" 
DEY 92 34 42. 

The sum of these is 180 o 26, 

and by calculation we find that the spherical excess is inappreciable, which 
leaves the triangular error 

+ 26". 

Now we cannot solve the triangle until it has been made into a perfect 
triangle, whose angles add up to 
exactly 180°. If we are concerned 
with this triangle alone, the best 
thing that we can do is to divide up 
the error into three equal parts and 
apply one to each of the angles, so 
that the sum of the thus corrected 
angles is exactly 180°. 

This being done we can find the 
length of either of the sides EY ox 
DY, being given the other side DE 
and the angles of the triangle. 

For by elementary trigonometry 

DY _ s\nDEY 
DE~ sin DYE' 




Fig. 22. 



whence D Y= DE cosec D YE sin DE Y, 

and similarly EY=DE cosec DYE s'm YDE. 

Thus either D Y or EY is easily found. 

Distributing the excess of 26" over the three angles we have for the 
corrected values : 

Angle at D 55° 28' 7" 

Y 31 57 20 

^ 92 34 33 

180 o o 



158 TOPOGRAPHICAL SURVEY 

Thus if log /?£■ = 3-8337549, 

\ogDY=\ogDE 3"8337549 

+ log cosec Z> Kfi" o'2763299 
+ \og sm DEY i'99956io 

4-1096458 
and similarly log £"1^=4-0259149. 

This example is taken from the work of a vacation survey class in the 
Isle of Wight. 

Proceeding to the next triangles we can find FY from the triangle 
FYE, since YE has been found ; or we can find it from the triangle FYD 
since YD has been found. We thus arrive at two values of FY which will 
probably not agree precisely with one another, because of the arbitrary 
character of the corrections which have been applied to reconcile the slightly 
erroneous angles in the triangles. And if we had gone a different way round, 
deriving FY through FD or FE we should have obtained other slightlj^ 
differing values of FY. 

In ordinary topographical work not of high precision we shall take the 
mean of the various values we obtain for any side ; and proceed. But in 
precise work this is not possible, and some way must be found of determining 
such a set of corrections to the angles that we arrive in the end at the 
same result precisely, whichever way we go round. This is called the 
adjustment of the quadrilaterals, and is a process much too elaborate to be 
described here. 

Closing one base on another. 

By the above process we may start from the measured length 
of one base and calculate right through the chain of quadrilaterals 
until we arrive at another measured base. We shall then have 
two values for this base : the directly measured value ; and the 
value carried through by calculation from the first base. These 
two values will generally differ from one another by a slight 
amount ; and it is usually assumed that the former is correct. 
We have then to investigate the corrections that are to be 
applied to the triangulation, in order to make the measured and 
the calculated lengths of the base agree with one another. It 
will be evident that this is a more elaborate piece of adjustment 
than the first, and far more unsuitable for description here. 

Calculation of the geographical positions of the triangu- 
lation points. 

For general purposes the most convenient way of defining 
the position of each point is to give its latitude and longitude. 



TOPOGRAPHICAL SURVEY 159 

We have determined an initial latitude and longitude of a 
station A, the azimuth of the line AB, and the length in feet of 
AB. The problem is to determine the latitude and longitude 
of AB, and the azimuth of A at B. For the purposes of precise 
survey it is not sufficient to resolve AB along and at right 
angles to the meridian through A, and conv^ert these resolved 
distances into differences of latitude and longitude. We have 
to take account of the curvature of the Earth, and of the fact 
that owing to its spheroidal shape the curvatures along and at 
right angles to the meridian are not the same. The necessary 
formulae are somewhat complicated, and the analysis by which 
they are established still more so. It must be sufficient to say 
here that the Survey Tables of India, reproduced in extended 
form in the Textbook of Topographical Surveying, pp. 209 et seq., 
have reduced the computation to a simple form, by a process of 
great ingenuity. 

We should note that this process demands a knowledge of 
the size and shape of the Earth, as a basis for the tables. 

The calculation gives the differences of latitude and longitude 
between A and B ; which being added to the co-ordinates of A 
give those of B. It gives also the azimuth of A from B, tech- 
nically called the 'reverse azimuth,' which is not quite 180° 
different from the initial azimuth, on account of the convergence 
of the meridians towards the pole. 

Now to proceed from B to C : We have the measured angle 
ABC and the azimuth of BA, from which we deduce the azimuth 
of BC, and the process of carrying on from B to C proceeds as 
before. 

Thus we obtain the geographical positions of all the triangu- 
lation stations. Any selection of them can now be plotted on 
any plane table sheet in the manner to be described presently. 

Calculation of rectangular co-ordinates. 

If however the area surveyed is small, and it is a question 
only of plotting a single sheet or small number, it may not be 
worth while to perform the above calculation of the latitudes 
and longitudes. For the purpose of plotting the plane table 
sheets it is sufficient to calculate the rectangular co-ordinates of 



i6o TOPOGRAPHICAL SURVEY 

the other stations with respect to axes through the initial station, 
treating the triangulation as if it were on a plane instead of 
being on the spheroid. This is simpler to calculate, but we 
shall see that it is not so simple to plot ; and there is great 
difficulty eventually if geographical positions should be wanted 
after all. 

Construction of the plane table graticule. 

The plane table graticule is a construction of meridians and 
parallels drawn on the table, so as to permit the plotting of any 
station whose latitude and longitude have been derived from the 
preceding calculation. The projection upon which the graticule 
is drawn is an approximation to the polyconic projection. The 
quantities required are derived from tables such as those given 
in the Textbook of Topographical Surveying, pp. 227 et seq., and 
the method of construction is given on p. 93. See also the 
author's Map Projections, pp. 58, 118. This work can be done in 
the field, with only the sight rule of the plane table and a pair 
of dividers. When the graticule is plotted it is easy to inter- 
polate and plot any station whose geographical position has been 
determined. 

At first sight this method may seem to be elaborate, and the 
beginner may imagine that something much simpler might be 
devised to serve its purpose. It will be found, however, that for 
the orderly conduct of a regular survey nothing less systematic 
will serve. Generally speaking, when the triangulation is com- 
plete and calculated, the work of plane tabling the detail is 
divided up between a number of surveyors, who undertake each 
a definite block bounded by certain meridians and parallels. 
Each plane table will be plotted so that it includes an area 
somewhat larger than that assigned to the particular table ; and 
the triangulation points will be plotted all over the sheet. To 
have these well determined points all round outside the area 
actually being mapped is a great convenience. 

Mapping the detail by plane table. 

When the surveyor goes out into the field with his plotted 
sheet he first visits some of the principal points, sets up the 



• TOPOGRAPHICAL SURVEY i6i 

table there, and sights round to the other points within view, to 
see that the rays come right, and that no mistake has been made 
in the plotting. At one of the stations, while the table is set, 
he puts on the compass lines for the trough compass. He also 
takes the opportunity of drawing rays to prominent objects 
which will serve as intersected points. 

This being done, the work of mapping proceeds as in 
graphical plane tabling, and we need not repeat what has been 
said on the methods of fixing by resection. Since the positions 
of the calculated points are correct far within the limits of visible 
error, the general accuracy of the whole will be much better than 
in the graphical process, and a second resection should always 
give an exact cut of the three rays, without any triangle of 
error. 

The determination of heights and contours will be very 
much more exact than in the graphical process, because they 
will be all based on the theodolite heights of the triangulation 
stations. 

The spot heights at the resected points will be determined 
with the Indian pattern clinometer (see Plate XV), which consists 
of a brass bedplate with a bubble and levelling screw, set up 
along the ray on the board, and levelled. Two leaves standing 
up at either end of the base plate carry respectively a small 
sight hole, and divided scales of degrees, on one side, and of 
tangents of degrees, on the other side of a vertical slit. The 
observer, looking through the sight hole at the distant point, 
reads off the tangent of the elevation or depression of the 
distant point. He then scales off its horizontal distance, multi- 
plies it by the tangent, and obtains at once the vertical interval 
between the plane table and the distant station. He must not 
forget to take account of the height of the table above the 
ground, in calculating the spot height. 

This process is about ten times as accurate as determining 
spot height with the Watkin clinometer ; and being based upon 
accurate fundamental heights, it gives points for contouring with 
all the refinement which can be desired, except for detailed 
engineering. 

H. M. S. II 



1 62 TOPOGRAPHICAL SURVEY 

When the spot height is fixed, the slopes are observed with 
the scale of degrees on the other side of the opening in the vane, 
and the process of calculating mentally the places and spacing 
of the contours are almost exactly similar to those which we 
have already described fully in Chapter V, pages 109-112. 

When the section allotted to the surveyor is complete he inks 
in all the lines and figures which are to stand, clears up with 
rubber all those which are not required, and sends in the field 
sheet to headquarters. The great advantage of this system is 
easily seen. The field work comes in block by block all ready 
for the draughtsman, who has only to redraw it on the finished 
sheet, when it is ready for reproduction. There is very little 
possibility of confusion or misunderstanding, or of some portion 
of the work being missing. All this tends strongly to good 
order, efficiency, and economy in the operations of the survey. 

Precise traversing. 

It must always be remembered that in certain types of 
country triangulation and plane tabling are impossible, as on 
the Gold Coast, a nearly flat and densely forested region, where 
it is impossible to obtain a view of any importance. In such 
country it is necessary to construct a framework of traverses, 
run with the theodolite and steel or invar tape along lines of 
clearance cut through the forest. This is expensive, and 
exceedingly unsatisfactory, because in a few months the lanes 
are grown up again, and the labour seems to be lost. 

The methods of work vary much in different countries, and 
for an account of them we may refer to such books as the 
Handbook of the Southern Nigeria Stcrvey. 

The process of topographical survey which we have described 
here is that which, with small differences, is in use in all the 
principal surveys of the world. It is admirably suited to the 
rapid production of maps on topographical scales, especially 
where the detail is not too crowded. 

It is not, on the other hand, so suited to the production of 
large scale cadastral maps showing intricate boundaries of 
property. In such cases it is usually necessary to break down 



TOPOGRAPHICAL SURVEY 163 

the triangulation into small triangles of about a mile a side, by 
the theodolite, and to cut these up in turn and fill in the detail 
with the chain. This was the method by which the whole 
of the detailed survey of the United Kingdom was carried 
out. It is very accurate, and very expensive. But it has no 
geographical interest, and we shall not consider it further in 
this book. 

The Ordnance Survey of Great Britain and Ireland, 

The beginnings of the Ordnance Survey may be traced to 
the Highland rebellion of 1745, when the Quartermaster General 
to the forces of the Duke of Cumberland made a map of the 
Highlands, which proved so useful that it was extended to the 
Lowlands, and the intention was formed of making a map of 
the whole kingdom. The project was continually interrupted 
by war, and not very much progress was made with it. 

In the year 1783 Count d'Adhemar, the French Ambassador, 
transmitted to Mr Fox a memoir of Monsieur Cassini de Thury, 
proposing to connect Greenwich and Paris by a triangulation, in 
order to determine the difference of longitude between the two 
Observatories. The British Government accepted the proposal, 
and entrusted to General Roy the task of planning and directing 
the enterprise. The first step was to measure a base on Houns- 
low Heath. Thence a chain of triangles was carried across the 
Surrey Hills and through Kent to Dover, from which the con- 
nection was made to Boulogne, Calais, and Dunquerque. It is 
interesting to notice that in this early work the observations 
were made to lamps, at night. 

These operations made it possible to bring out a really 
accurate map of Kent. Immediately the demand arose for 
equally good maps of Sussex and of Essex ; the Admiralty 
required that the chain of triangles should be continued west- 
ward to the Land's End and Scilly, for the improvement of the 
Channel Charts; and then began that movement in favour of a 
complete survey of the Kingdom, for which General Roy had 
been looking ever since his early experience in the Highlands. 

The principal triangulation of the United Kingdom occupied 
roughly the first half of the nineteenth century. Unlike modern 



i64 TOPOGRAPHICAL SURVEY 

triangulations of the first class, it was extended over the whole 
country, and not merely confined to chains along the meridian 
and parallel. It was made with the celebrated three foot theodo- 
lites constructed by Ramsden, 

The survey of a thickly settled country cannot be conducted 
without the right of access to property of every kind ; and in 
the English survey this right was interpreted very liberally. A 
great platform was erected over the Cross of Saint Paul's Cathe- 
dral in London, and a section of the spire of Norwich Cathedral 
was temporarily removed to make a station for the instrument. 
These stations are marked beyond any probability of loss. But 
the stations in the open country are not so well identified, and 
some of them could not be recovered if they were required for a 
revision of the triangulation. More unfortunate still, one end of 
the principal base on Salisbury Plain is lost, by the mischievous 
enterprise of some persons unknown, who dug up the bronze 
gun which was sunk in the ground to serve as a terminal. It is 
now generally recognised that the right way to preserve triangula- 
tion stations and principal bench marks of the levelling is to buy 
the small plots of ground on which they stand, fence them in, 
and entrust them to the care of the local authorities. 

The connection between Wales and Ireland involved great 
difficulty owing to the rarity with which very long rays can be 
observed in the moist climate of the west. The difficulty was 
overcome in the end by the invention of the limelight, and 
observation at night. The extension northwards to the Shet- 
lands was possible only because of the fortunate situation of the 
small islands Faira and Foula. Further extension to the Faeroes 
is impossible. 

The triangulation of the United Kingdom rests on the two 
bases of Salisbury Plain and Lough Foyle ; it was not found 
possible to measure a good base in Scotland. Indeed it was the 
opinion of the surveyors that there was not in the whole of Scot- 
land a site on which a base could be measured with possibility 
of connection to the triangulation. Modern improvements in 
base apparatus have at last removed from Scotland this reproach. 

The ' breaking down ' of the principal triangulation into the 
smaller secondary and tertiary triangles eventually covered the 



Plate XXI 




I. Measurement of the Lough Foyle Base. 





2. The Great TheodoHte. 



3. Scaffold on Gravelines Church for 
the connection with France. 



nee Survey. Principal Triangiilation. 



TOPOGRAPHICAL SURVEY 165 

country with a net of triangles averaging little more than a mile 
a side. So minute a subdivision was required because the detail 
was all to be fixed by chaining. It is a peculiarity of the survey 
of the United Kingdom that not only the horizontal detail, but 
also the contours, are all chain surveyed. The great expense of 
accurately surveyed contours made it impossible to place them 
as close as was desirable ; and it is now recognised that less 
accurate contours at a smaller vertical interval would have been 
more valuable than the less frequent levelled, pegged, and 
chained contours which must in course of time become obsolete 
by changes due to weathering and to cultivation. 

The latest report of the Ordnance Survey, dated 19 12 May 28, 
gives much interesting information on the present state and 
future intentions of the Department. The Survey is now 118 
years old. In that time it has completed the trigonometrical 
framework of the United Kingdom, which occupied altogether 
some sixty years ; it has produced the one-inch map of the 
whole Kingdom, and revised it twice ; the six-inch and twenty- 
five inch maps of Great Britain, with one revision ; and the six- 
inch map of Ireland with one revision. The twenty-five inch 
map of Ireland will be finished in 19 14. 

A great part of the work of the Survey now consists in the 
systematic revision. It is now the rule that no large scale map 
shall be more than twenty years unrevised, and that the small 
scale maps shall never be fifteen years out of date when they are 
issued. And the more important alterations, such as new rail- 
ways, are shown very nearly to date. With the rapid extension 
of industrial development the amount of detail to be shown, and 
the complication of the map, become continually greater. 

" A hundred and seventeen years ago the surface of the three 
Kingdoms presented an appearance on the maps very different 
from what we are accustomed to, and this is of course especially 
the case in and near what are now the great centres of popula- 
tion. We must picture a map which shows no railways, no 
system of metalled roads, no post or telegraph offices, few factories, 
a map dotted with small towns, showing by their plans their 
medieval structure. Yet in the country we should find the 
boundaries of counties and parishes but little changed, and 



i66 TOPOGRAPHICAL SURVEY 

we should find the same immemorial hedges." {O. S. Report, 
1912.) 

After a rather long repose the scientific side of the survey 
has been awakened within the last few years, and important 
works are in progress. Owing to its early date, and to its 
pioneer character, the principal triangulation of the country, 
though absolutely sufficient for the practical needs of mapping, 
is possibly below the standard required in modern discussions 
of the figure of the Earth ; but owing partly to the difficulty 
of measuring a base in Scotland, it was not easy to define 
precisely how far it falls short of the desired standard. To test 
this matter a base has been measured at Lossiemouth, and a 
portion of the triangulation is being re-observed in connection 
with it. At the same time all the principal stations of the 
triangulation are being examined, and re-marked in more 
permanent fashion than was thought necessary at the time 
when they were occupied for observation. 

" So far as the mean sea level is concerned, the datum in use 
on Ordnance Survey maps at present has no scientific value. 
Steps are being taken to determine with all available precision 
satisfactory values of the mean sea level in Cornwall, and on the 
North Sea. The revised network of levels and the precise 
values of mean sea level will not only serve practical purposes 
better than these have been served in the past, but will provide 
data for the determination of the vertical movements of that 
portion of the earth's crust which is Great Britain." {O. S. Report, 
1912.) 

An important feature of the new programme of levelling 
is the provision of fundamental points based on the solid 
rock. 

The cost of the Ordnance Survey is nearly a quarter of a 
million per year, and about one tenth only of this is received 
from the sale of maps to the public. But on the other hand, 
it is probable that the amount saved to the public by the exis- 
tence of the Ordnance Survey maps is several millions per year. 
And the work of Government could not proceed without the 
Survey. The value of maps and plans furnished to Government 



TOPOGRAPHICAL SURVEY 167 

Departments during the year 191 1 — 191 2 was more than three 
times the value of those bought by the public. 

India. 

The Survey of India has a long and honourable history, and 
no country of the world has contributed more to the advance- 
ment of geodesy, the thorough organisation of topographical 
survey, or the methods of work in difficult frontier country. 
Only in the methods of map reproduction has the Survey of 
India failed to maintain the highest level ; and great improve- 
ments have been made in this respect in recent years. The 
frequent references to Indian methods in the British official 
textbooks show how great an influence this celebrated depart- 
ment has exercised on the survey work throughout the Empire. 

Canada. 

Until within the last few years the great amount of survey 
that was done was for special purposes, and since it was not 
done under the control of any one authority, nor in any systematic 
manner, the greater part of it was inevitably wasted, from the 
point of view of the production of a topographical map of the 
country. This is now happily changed. A geodetic survey is 
in progress under the direction of the Chief Astronomer and 
the topographical survey is being pushed forward by the Militia 
Department, while the reproduction of the maps has been under- 
taken by the Geographical Section of the General Staff in 
London. The diagram of sheets published is to be found in 
the Catalogue of Maps published by the latter department. 

Australia. 

The conditions in the Commonwealth very much resemble 
those in Canada. A great deal of miscellaneous survey has 
been carried out without much result in the production of topo- 
graphical maps. A good deal of primary triangulation is now 
being done, but there is not yet much information available, and 
it does not appear that the publication of maps has yet been 
begun. 



1 68 TOPOGRAPHICAL SURVEY 

South Africa. 

The geodetic triangulation is complete, and a great part of 
it is included in the arc of the 30th meridian, to which reference 
has already been made. The Orange Free State has been 
surveyed topographically on the basis of the geodetic survey, at 
the joint expense of the British and the Colonial Government. 
A reconnaissance survey of Cape Colony has been made in part, 
but this is now suspended. No topographical survey exists in 
Natal, the Transvaal, or in Rhodesia, and the want of such a 
survey is not only a danger from the point of view of defence, 
but is a standing obstacle to the development of the country. 

British Tropical Africa. 

The tropical possessions in Africa are in a much more for- 
ward condition, in regard to survey, than the much older states 
to the south. At first much money was spent rather ineffectively 
in desultory survey, but great progress has been made since the 
establishment of the Colonial Survey Committee in 1905. It is 
the duty of this committee to make such recommendations as 
will ensure the rapid and economical prosecution of accurate 
surveys where these are required, and the rendering the results 
available as speedily as possible for use by the Home Govern- 
ment, the Colonial Governments, and the public. 

This committee publishes an annual report, which is full of 
the most interesting information, and should be read by all 
students who are interested in the survey of the Empire. In the 
first report, dated August 1906, special attention was drawn to 
"the importance of enforcing the rule that work should be taken 
up systematically by blocks according to a definite programme. 
This is a principle which cannot be too strongly insisted on, but 
which has been largely neglected in the past ; the observance of 
this principle is a fundamental condition of efficient and econo- 
mical work." The excellent results of the criticism exercised by 
the committee may be seen in the very satisfactory records of 
progress in the later reports. 

The work of the Colonial Survey Committee was at first 
principally in tropical Africa, but it has gradually extended its 
interest to other colonies and dependencies. 



TOPOGRAPHICAL SURVEY 169 

Boundary Surveys. 

The survey and delimitation of international boundaries in 
Africa have been the means of surveying many of the outlying 
portions of the tropical protectorates, and the great variety of 
the conditions to be faced has led to great improvements in the 
technical methods employed. It is unfortunate that there is not 
available any general account of these operations, which are of 
the highest interest. 

A detailed summary of the length of each boundary, the 
date of its survey, ratification, and demarcation, is given in the 
Colonial Survey Report. The general course of the operations 
is as follows : 

"First there is an international agreement drawn up on broad 
lines ; each government then appoints Commissioners, who meet 
at one end of the boundary and march along it, exploring 
and mapping the boundary zone. The Commissioners, having 
arrived at the other end, agree upon the geographical position 
of the principal features and decide upon the details of the 
frontier, paying special attention to the incidence of tribal 
boundaries, and to the future nationality of the villages. They 
then march back along the line, erect pillars, and inform the 
chiefs. The protocol in duplicate is drawn up and signed, and 
each Chief Commissioner forwards the protocol and maps with 
a report to his Government. The protocol is then approved by 
the two Governments, and in some instances a fresh agreement 
on the terms of the protocol (with perhaps some minor modifi- 
cations) is drawn up and signed by the representatives of the 
Governments." 

Great Britain is interested in about 17,000 miles of boundary 
in Africa, of which about 10,000 have now been surveyed, 
principally within the last fifteen years. The result of this 
activity is that the perimeters of our African possessions are 
more accurately surveyed than the interiors, and the land 
boundaries better than the sea coasts. 

In other parts of the world also the demarcation of boundaries 
has involved interesting surveys, notably on the Alaska Boundary, 
the boundary between Chile and Argentina, surveyed by the 



I70 TOPOGRAPHICAL SURVEY 

officers of the British Arbitration Commission, and the Akaba 
boundary between Egypt and Sinai. 

These have provided instances of the delicacy with which 
the fixing of an international boundary must be conducted, or 
the dangers which arise from any looseness or ambiguity in the 
definitions, so long as there is not a chain of conspicuous beacons 
erected at intervals along the boundary with the consent of both 
parties. There are now no "hinterlands" in Africa, the partition 
of the continent is complete, and the boundaries are well defined 
by treaty or convention. It is highly satisfactory to know that 
the actual delimitation of these boundaries is making such rapid 
progress that there will soon be very little left unmarked. 



CHAPTER VII 

GEODETIC SURVEY 

The present meaning of the word Geodesy is the same as 
the old meaning of the word Geometry : the measurement of 
the Earth. And it is a great pity that the word is sometimes 
used, in examination schedules, to mean elementary survey. 

Figure of the Earth. 

The principle which underlies the measurement of the 
Figure of the Earth is exceedingly simple. 

Suppose first that the Earth is, to the best of our knowledge, 
spherical ; and consider how we should measure the radius of 
the sphere. Take two stations on the same meridian, and 
determine the latitude of each. This gives the distance between 
the two stations in angular measure on the sphere. Now, by 
triangulation, measure the distance between the two stations in 
terms of the unit of length that we prefer, say metres. We then 
have the result that so many metres are equivalent to so many 
degrees, minutes, and seconds of the arc on the sphere. If the 
difference of latitude is ;/', and the distance between the stations 
along the meridian is M metres, then the radius of the meridian 
in metres is given by the equation 

Radius = M co?,^c i" jn. 

This is the principle of the method used by Eratosthenes in 
his celebrated attempt to measure the Earth, in the third 
century B.C. 

If similar operations carried out in many different latitudes 
on various meridians gave always the same value for the radius, 



172 GEODETIC SURVEY 

we should have the clearest evidence that the Earth was a true 
sphere. But in fact we get different values for the radius when 
we determine it in different places. This was suspected in the 
latter part of the seventeenth century ; but the errors incidental 
to early operations of the kind led to some confusion ; and it 
was not until the celebrated measures made under the auspices 
of the French Academy in Peru and in Lapland had been 
brought to a successful conclusion that the law of the variation 
was definitely established for the northern hemisphere. The 
further one goes north, the larger is the distance corresponding 
to a degree of latitude : the flatter, therefore, is the Earth. 

The measures made in Peru and in Lapland, combined with 
those made in France, were consistent with the hypothesis that 
the Earth is a spheroid of revolution, or, in other words, that all 
the meridians are similar ellipses. They were consistent with 
this idea, but they were by no means sufficient to prove it ; and 
in the middle of the eighteenth century grave doubt was cast on 
the matter by the result of the Abbe de Lacaille's measure of 
an arc of meridian at the Cape of Good Hope, which seemed 
to show that the southern hemisphere was prolate, the degree 
decreasing in length as the pole was approached. 

It was some time before the explanation of this difficulty 
was discovered ; and in the meanwhile a somewhat similar 
discrepancy had been found in England, the curvature of the 
southern half of England appearing to be less than that of the 
northern half 

Deviations of the vertical. 

The origin of these abnormal results is in the existence of 
local deviations of the vertical, which have been mentioned 
already in Chapter VI, page 142. The latitude of any station is 
the inclination of the Earth's polar axis to the horizontal plane of 
the station. The horizontal plane is the plane at right angles to 
the direction of gravity. The direction of gravity is determined 
by the distribution of matter within the crust of the Earth. If 
this distribution is abnormal in the neighbourhood of a station 
the horizontal plane is no longer a tangent plane to the spheroid 
which represents the general form of the Earth ; and if such a 



GEODETIC SURVEY 17 z 

place is chosen by bad luck as one of the terminals of an arc 
of meridian the curvature of the meridian deduced from these 
measures is not representative of the general average curvature 
of a meridian in that latitude. 

We have said that the direction of the vertical is influenced 
by the distribution of matter within the Earth's crust. It is also 
of course affected by the attraction of the visible mountain 
masses above the level surface. But these latter can be allowed 
for ; and when this is done it nearly always happens that the 
visible masses prove to be quite insufficient to account for the 
results obtained. Indeed it not infrequently happens that the 
deflection of the vertical is in the direction opposite to that 
which would result from the attraction of the visible mountain 
masses alone. Such is the case at Dunnose, the station in the 
Isle of Wight which is the southern terminal of the arc of 
meridian of Great Britain. Here there is high down to the 
north, and the English Channel to the south. The density of 
the water is only about two-fifths that of the surface rocks, and 
it might be expected that in such a situation the direction of 
gravity would deviate away from the sea, and towards the land 
masses to the north. At this station an opposite effect is found. 
The direction of gravity is deflected to the south ; the horizontal 
plane is tilted to the north ; the angle which the Earth's axis 
makes with this plane is diminished ; the latitude of the place 
comes out too small ; the amplitude of the arc of latitude is 
increased and finally the southern half of the British arc of 
meridian appears to be flatter than the northern half. 

What happens at Dunnose happens to a greater or less 
extent at most stations. These deviations in the direction of 
gravity are the most disturbing factor in geodetic work ; and 
we will discuss them a little more fully before we deal with 
modern determinations of the size and shape of the Earth. 

The attraction of the Himalayas. 

The problem of the effect of the Himalayas on the direction 
of gravity in India has been present continually to the Indian 
surveyors. North of the Indian arc is the immense mass of the 
greatest mountain range in the world ; to the south the Indian 



174 GEODETIC SURVEY 

ocean is very deep, and the consequent deficiency of density 
considerable. It might be expected that in India the direction 
of gravity would be deflected towards the north; and calculation 
shows that the effect of the visible excess of density to the 
north, the visible deficiency to the south, should extend all over 
India. 

A great number of careful determinations of latitude were 
made at stations along the great arc of meridian, but the 
expected effect was not obtained. The discordances between 
the astronomical and the geodetic latitudes were considerable ; 
but they did not fit in at all well with the deviations which the 
visible masses should have produced. It appeared that some 
cause was at work which in great part annulled the effect of the 
mountain attraction. This was the first indication of the law 
which now plays so large a part in these enquiries, that in some 
way the expected effect of mountain masses is compensated, as 
if there were underlying deficiencies of density which nearly 
balanced the visible masses. 

About the year i860 Archdeacon Pratt, of Calcutta, a dis- 
tinguished mathematician from Cambridge, applied himself to 
the mathematical investigation of this problem, and arrived at 
the above result, that the attraction of the mountains is not so 
great as their visible masses would lead one to expect. The 
then Astronomer Royal, Sir George Airy, proposed to explain 
this in the following way : Conceive that the Earth is composed 
of a solid crust about forty miles thick, with a liquid below. 
The strength of the crust would not be nearly sufficient to 
support the weight of the superincumbent mountain masses ; 
therefore there must be some support for them, and this may be 
in the form of protuberances beneath the mountains, of the 
lighter crust into the denser liquid below. In such a way the 
mountains would be in equilibrium because they are practically 
floating like icebergs in the ocean, buoyed up by the intrusion 
of their " roots " into the liquid. 

This "roots of the mountains" theory has been the subject of 
much interesting discussion, especially by the Reverend Osmond 
Fisher, in his Physics of the Earth's Crust. Mathematicians 
have in general felt themselves compelled to reject the internal 



- GEODETIC SURVEY 175 

fluidity of the Earth, on account of certain tidal phenomena, 
into which we can hardly enter. But the important idea that 
the principal mountain masses are nearly in equilibrium, their 
visible excess of weight balanced by invisible defect of density 
below, as if they were floating, has by gradual steps become an 
established principle of geodesy. 

If the visible excesses of dense material in the mountains are 
counterbalanced by deficiencies underneath, it is clear that we 
may expect also that the visible deficiencies of matter in the 
oceans should be balanced by excesses of matter in the ocean 
beds. Evidence for this supposition cannot be found however 
in the observations for latitude, so well as in the conclusions to 
be drawn from the determinations of gravity by the pendulum, 
to which we must now refer. 

Gravity survey with the pendulum. 

The mathematical theory of the attraction of a spheroid at 
any point of its surface, or at an external point, provides a 
formula which expresses the force of gravity, and thence the 
time of oscillation of a pendulum of known length, at any place. 
Knowing the shape of the Earth, we can predict the rate of 
swing of the pendulum ; and alternatively, it is evident that if 
we carry an invariable pendulum about the world, and determine 
the time of its swing at different places, we have a means of 
determining the figure of the Earth independent of the triangu- 
lation and latitude method explained above. When sufficient 
observations were accumulated it was found that the two inde- 
pendent methods of arriving at the ellipticity of the Earth gave 
results which were in tolerable agreement, though they were 
not identical. For the moment the discrepancy need not con- 
cern us. 

But it was also found that the pendulum observations on 
high mountains, as in the Himalayas, gave peculiar results. It 
is easy to calculate the intensity of gravity at a given height 
above the surface of the Earth, and to allow for the increase 
which should be due to the mass of the mountain on which the 
pendulum is established. But observation discloses the remark- 
able fact that the mountain mass itself has not the expected 



176 GEODETIC SURVEY 

effect ; the pendulum swings pretty much as if it were somehow 
supported at the height of the mountain, but unaffected by the 
mountain mass. In other words, the attraction of the mountain 
is more or less compensated. 

Further, it was pointed out by the French geodesist Faye 
that a similar effect is found on oceanic islands : similar in 
cause, though opposite in its immediate effect on the time of 
swing of the pendulum. On those volcanic islands which rise 
steeply from deep ocean the force of gravity, as determined by 
the pendulum, is in excess, the excess being about that amount 
which can be attributed to the mass of the island standing above 
the ocean floor. In other words, if the pendulum could be 
swung on the surface of the sea, without the material support of 
the island, then the time of swing would be normal. 

This important result has been confirmed, within recent 
years, by the work of Hecker, who has made several long 
voyages, including a circumnavigation of the world, comparing 
all the while the readings of a large number of mercurial 
barometers and of boiling point thermometers. Both these 
instruments determine the pressure of the atmosphere; but 
whereas the height of the barometer is affected by the intensity 
of gravity, the boiling point of the thermometer is not. It may 
well seem remarkable that this method can be made of delicacy 
sufficient for the purpose in view, and there are indeed many 
instrumental difficulties to be overcome. But these observations 
seem to place beyond much doubt the result suggested by the 
island pendulums, that over the surface of the ocean gravity is 
normal ; it is not diminished as might be expected by the small 
density of the water as compared with rock ; and the simplest 
explanation seems to be that the rocks below the ocean floors 
are extra dense, to balance the deficiency above. 

Gravity in India. 

Recent very interesting work of the Survey of India shows 
that the problem in India is more complicated than had been 
supposed. In the foothills of the Himalayas the "compensation" 
is partial ; immediately to the south of the mountain range the 



Plate XXII 





n 


Ti- 


- 




i 




^ Mil 






I. Half-second Pendulums. 2. Clock and Flash Box. 

Gravity S^ivvey. 




urvey of India. 



3. Latitude with Zenith Telescope. 



GEODETIC SURVEY 177 

compensation is more than complete, so that there is a defect of 
density underlying these regions. 

A few figures will serve to show the nature of these results. 

All observations are referred to Kew as the base station. The value of 
g, the acceleration due to gravity, is taken to be 981 •200 centimetres at Kew. 
The Indian pendulums were swung at Kew, and the mean time of vibration 
was o"5o67ooi seconds. The same pendulums swung at Dehra Dun gave for 
the mean time of vibration o"5072528 seconds. That is to say, as compared 
with Kew they lost one swing in something less than ten thousand. Now 
by the theory of the pendulum the square of the time of oscillation multiplied 
by the value of gravity is constant for all stations. Hence we deduce for 
Dehra Dun the value _^=979'o63 cm. 

This has now to be corrected for the diminution of gravity due to the 
height of Dehra Dun above sea level. Without allowing for the attraction 
of the ground above sea level the reduction is +o'2io. The correction for 
the attraction of the "visible masses" is — 0*075 ; so that the value at sea 
level is 979* 198 cm. But the sea level value computed for Dehra Dun from 
Helmert's general theory for the whole Earth is 979'324, which is greater 
than the observed value even without the allowance for the visible masses. 
Instead of having to allow for the attraction of the equivalent of a plateau 
some 2200 feet high, it appears that the effective attraction is as if a depth 
of 3600 feet were annihilated. There is a large deficiency of gravity, there- 
fore, at Dehra Dun. 

Similar observations made at many stations show that while 
in the foothills of the Himalayas the attraction of the mountain 
masses is partially, but not fully compensated, immediately to 
the south is a " ditch " of deficient density, before the attrac- 
tion becomes normal. It is clear that results of this kind must 
eventually throw much light on all questions of the theory of 
the Earth's interior, and especially on the methods of mountain 
formation. They have a general interest outside their technical 
geodetic importance, and for this reason we have dealt with 
them in some detail. 

The theory of " isostasy." 

The convergence of these various lines of investigation to 
the same point seems to have fairly established the general law 
of balance : where there is excess of mass above it is balanced 
by deficiency below, and vice versa. To this condition the 
American geodesist Major Button gave the name "isostasy," 
H. M. s. 12 



178 GEODETIC SURVEY 

signifying that the crust of the Earth is in a general condition 
of hydrostatic equiHbriunfi, as if it were floating, though it is not 
necessarily doing so. 

The question then arises, to what depth must one go before 
this state of balance is fully established? Very elaborate investi- 
gations on this subject have been made of late years by the 
United States Coast and Geodetic Survey. Starting with the 
assumption that there must be some definite depth at which 
the compensation becomes complete, they have tried to deter- 
mine the depth, and have arrived at the result 120 km. It is 
quite impossible to deal here with the methods of this exceed- 
ingly elaborate and arduous piece of work ; and it does not 
seem to the author to be sufficiently established that there is 
any one depth at which the compensation becomes complete. 
Much light will be thrown upon this question by the discussion 
of the Indian results which has been undertaken to test the 
applicability of the hypothesis to India. 

It should be understood that the theory of isostasy does not 
require that the compensation is locally complete everywhere, 
but only that there is general compensation of the principal 
masses which are raised above the Earth's surface. In India 
great complications are introduced by the existence of a 
subterranean range of excessive density running parallel to 
and south of the Himalayas, with a "ditch" of deficient density 
between this and the mountains. 

The form of the ocean surface. 

In connection with this subject of mountain attraction it is 
natural to speculate what effect is produced upon the form of 
the ocean surface by the attraction of great mountain masses. 
Several calculations have been made which show that if the 
mountains can exert the full effect that their visible masses 
entitle them to, the elevation of the free surface of the ocean 
must be considerable. Colonel Clarke {Geodesy, p. 94 and 
following) gives a method of calculating the order of the effect 
upon the height of the sea surface produced by the attraction of 
the Himalayas, and shows that it might amount to as much as 
600 feet. " This calculation," he proceeds, " shows us that large 



GEODETIC SURVEY 17^ 

tracts of country may produce great disturbances of the sea 
level, but it is at least questionable whether in point of fact they 
do." The compensation of the mountain masses nullifies the 
effect in great part, we may be sure, and leaves little scope for 
the existence of great differences in the sea level radii of the 
Earth. 

Nevertheless it is common to meet in books the statement 
that the sea level at Calcutta is about 330 feet higher than it is 
at Cape Comorin ; and that the sea on the Pacific coast of 
South America, close under the Andes, is 2000 feet higher than 
it is at the Sandwich Islands. These statements are based on 
calculations such as Colonel Clarke gives ; but they are some- 
times said to be supported by the results of direct levelling. 
Such a statement is on the face of it absurd. The surface of the 
sea must be a level surface in the sense that spirit levelling from 
one point to another could give no evidence of rise or fall. Any 
attraction of mountain masses which changed the form of the 
sea surface would have an equivalent eff'ect on the results of the 
instrumental levelling. 

Geodetic measure of an arc of meridian. 

From what we have seen of the effect of local irregularities 
of gravity it is clear that no close accordance may be expected 
between the geodetic amplitude of an arc, measured by triangula- 
tion, and its astronomical amplitude, measured by determinations 
of latitude or longitude at each end. In order that the effects of 
these local abnormalities may be eliminated as far as possible it 
is usual to proceed in a way which may be described briefly 
as follows : 

Select as the initial point a station which seems to be free, 
as far as may be judged, from the influence of attraction by 
visible masses. Starting from this point we may from the 
triangulation calculate the latitudes of any number of points in 
the chain, using in the calculation tables founded upon one or 
other of the well-known results for the figure of the Earth : let 
us say Clarke's first figure. Compare these geodetic latitudes 
with the observed latitudes of the same points. The differences 
Geodetic minus Astronomical latitude 



i8o GEODETIC SURVEY 

are the material on which we shall found a revision of the figure 
which was adopted in the tables. 

If these differences are scattered at random, and show no 
tendency to grow steadily bigger or smaller, or first bigger and 
then smaller, they must be due in great part to local irregularities 
of gravity. But if they run in a systematic way the probability 
is that some modification in the adopted figure would make 
them smaller, and we proceed to find that figure which gives the 
best fit between the astronomical and the geodetic places. It 
is not hard to calculate the effect upon each comparison of a 
definite change in the assumed axes of the Earth, a change in 
its assumed ellipticity, and a correction to the adopted initial 
latitude. The various corrections will appear as the unknown 
quantities, with calculated numerical coefficients, in a series of 
equations, one for each latitude station. The solution of these 
equations of condition by the method of least squares gives the 
values of the corrections which reduce to a minimum the sum 
of the squares of the residual differences. And the theory of 
probability shows that this is the most probable result that can 
be found from the mass of somewhat contradictory material given 
by the observations. In other words one finds what corrections 
must be made in the original assumptions to produce the best 
fit between astronomy and geodesy over the arc in question. 

Similar considerations determine the method by which the 
observations of longitude and azimuth may be made to contribute 
to a revision of the size and the shape of the Earth. 

The outstanding discordances between the observed astronomical lati- 
tudes and the figure of the Earth which fits them best are by no means 
inconsiderable. For example, Clarke's 1866 figure is deduced from 40 latitude 
stations. The discordances of the British stations are as follows : 
Greenwich Geod. niimts Astron. +o"'94 
Arbury + i"'4o 

Chfton (Yorks) -2"-i9 

Kellie Law - o"'65 

Stirling — o"'24 

Saxavord +i"'9S 

The extreme discordances of all are at two Indian stations : 
Dodagoontah +3"'87 

Kalianpur — 3"'69 



GEODETIC SURVEY i8i 

If we remember that one second of arc in latitude is 
equivalent to one hundred feet it at once becomes clear that 
it is hopeless to try to make an accurate and consistent map on a 
basis of astronomical positions. Discordances of several hundred 
feet will arise, which are intolerable. 

The principal geodetic arcs. 

The first man to apply the principle of triangulation to the 
measurement of an arc was Snellius, whose work was published 
at Leyden in 1617. 

The first long arc of meridian was begun by Picard, and 
extended by the Cassinis. It had an amplitude of eight and a 
half degrees, and was at first supposed to show that the Earth 
was a prolate spheroid, contrary to the theory developed by 
Newton. This was early in the eighteenth century. 

In 1735 the French Academy undertook the measurement of 
the arc of Peru, and of another in Lapland. These, with the 
French arc mentioned above, provided the first accurate deter- 
mination of the figure of the Earth. 

In 1783 the triangulation of England was begun by General 
Roy, and connected with the French triangulation. 

In the nineteenth century the great meridian arc of Europe, 
on the 30th meridian of East longitude, was measured from 
Hammerfest to the mouth of the Danube, under the principal 
direction of the eldest Struve. Later the whole of Europe was 
covered with triangulation, which was then extended into Africa. 
Several arcs both of latitude and of longitude were measured in 
India; very considerable geodetic operations were undertaken in 
the United States; and at the end of the century the African 
arc of meridian, also on the 30th meridian East, was carried from 
the south of Cape Colony through the Transvaal towards Lake 
Tanganyika. 

At the present day there is great activity in geodetic work. 
A joint commission of Russians and Swedes have measured an 
arc of meridian in Spitsbergen, which is probably the most 
northerly arc possible, while the Service geogi'ciphique de VArmee 
has re-measured the "Arc of Peru," in territory which now is Ecua- 
dor. An attempt is being made to join up the triangulations 



1 82 GEODETIC SURVEY 

of India and Russian Asia. Egypt is actively pushing its portion 
of the 30th meridian arc southwards to the Great Lakes ; while 
another part of this arc has been measured in connection 
with a boundary survey on the Uganda-Congo frontier. The 
United States is steadily carrying forward its chains of triangles 
over the west and north, and Canada has begun its share of the 
triangulation of North America. Further south good work is in 
progress in Mexico and in Chili. The arc of the 30th meridian 
is of special importance because it is the longest latitude arc 
that can be measured on the Earth. There seems to be good 
hope that the African portion will be finished within fifteen or 
twenty years ; the greatest difficulty will be the junction be- 
tween Egypt and the Danube, through Turkish territory up the 
Eastern shore of the Mediterranean. 

A word should be said on the state of the British triangula- 
tion. It is the earliest in date of any of the great triangulations, 
and on that account is necessarily somewhat old fashioned. In 
a report on the triangulations of Europe, made to the Inter- 
national Geodetic Association by General Ferrero, the triangular 
error of the British work is given as about 3", with the inference 
that the work is not of sufficient refinement to be attached to 
the general European net. It seems likely that this criticism is 
not quite just. The triangulation of England covered the whole 
country, and much of it was difficult because the country was so 
flat. Many of the more unfavourable triangles entered scarcely 
at all into the arcs of meridian and of longitude, and it is hardly 
fair to burden these with the error of triangulation in other 
parts of the country. Within the last few years a base has been 
measured in Scotland by the Ordnance Survey, and some tri- 
angulation done to connect it with the existing net. This will 
provide a check upon the whole which will show how far the 
criticisms which have been passed upon it are justified. Should 
it be found that there is room for improvement it is much to be 
hoped that for the scientific honour of the country there will be 
no delay in the provision of funds for revision, so that Great 
Britain may take its rightful place in the arcs of latitude and 
longitude of Europe. 



GEODETIC SURVEY 183 

Geodetic triangulation. 

Geodetic triangulation differs from ordinary triangulation 
principally in the degree of refinement with which the angles 
are measured. 

Accuracy is increased by increasing the size of the theodo- 
lite, up to about a twelve inch circle. The modern theodolite of 
this size is more precise than the older instruments of much 
greater size, and it is doubtful whether anything is gained by 
employing larger instruments than the twelve inch. Accuracy is 
increased by increasing the number of observations of each angle, 
care being taken to begin each round of angles at a different 
part of the circle, so that errors of division are eliminated as far 
as possible. Greater care in the construction of beacons, and 
especially the use of self-centering beacons, as on the Egyptian 
Survey, add much to the accuracy of the result; so also in many 
places does the use of lamps at night, when refraction is more 
regular. 

Recent improvements in base measurement, and the result- 
ing possibility of measuring many more bases than formerly, are 
important aids to the control of the chains of triangulation. At 
the same time these instrumental refinements have much simpli- 
fied the work of adjustment of the triangulation ; while an even 
greater influence in the same direction has been the modern 
view that it is absurd to give different weights to the observed 
angles according as the separate determinations of them are 
more or less accordant among themselves. It is now realised 
that the errors to be feared are not so much the accidental 
errors that show themselves in roughness of individual measures, 
as the systematic errors that repeat themselves and thus escape 
notice at first. The tendency is therefore to simplify the re- 
ductions and to avoid the immense calculations which are so 
remarkable a feature of such work as the earlier Indian triangu- 
lations. Excellent examples of work thus simplified may be 
found in the published accounts of the geodetic triangulation of 
South Africa, executed by Colonel Sir William Morris under 
the superintendence of Sir David Gill, His Majesty's Astronomer 
at the Cape. 



i84 GEODETIC SURVEY 

The question arises often, under what circumstances is it 
worth while to undertake the expense of the greater refinement 
which shall make a triangulation suitable merely for the frame- 
work of the topography into a first class triangulation fit to take 
its part in the general problem of determining the size and 
shape of the World ? The answer must depend to a great extent 
upon the relation of the country in question to the principal 
land masses of the world. If it is isolated, and of moderate size 
only, then it can contribute little to the solution of the problem. 
But wherever there is a possibility of junction with other exten- 
sive work of the same kind it should be a point of honour with 
the country to contribute its share in the solution of the great 
problem. 

Principal chains. 

In the Ordnance Survey of England the primary, or geodetic 
triangulation covered the whole country. In modern practice 
the primary triangulation is run in chains along arcs of meridian 
and parallels of longitude, so that a large country is divided up 
into a series of quadrilaterals. On the framework thus built the 
secondary triangulation is hung. 

The chain is usually a chain of quadrilaterals, and complex 
figures are avoided as much as possible. Bases will be measured 
at least every two hundred miles along the chain. 

The test of the accuracy of the triangulation is, as we have 
seen, the size of the average triangular error; in the best modern 
work this is about o""/$. To obtain this remarkable degree of 
accuracy it may be necessary to observe each round of angles 
nine times. 

It is highly desirable that a preliminary calculation of the 
triangles shall be made as the work proceeds; this tends to give 
confidence in the success of the operations, and serves to detect 
at once any considerable error or unusual difficulty that may 
arise. But to carry out this programme requires a large and 
strong party. 

The astronomical observations. 

For precise work the observations for latitude will be made 
by Talcott's method, with the theodolite fitted to serve as a 



GEODETIC SURVEY 185 

zenith telescope. It is outside the scope of this book to enter 
into the details of this work. 

The azimuths will be determined in general from circumpolar 
stars at maximum elongation. 

The longitudes will be determined by the interchange of 
time by telegraph, or by wireless. The time observations will be 
made with portable transit instruments, and great precautions 
are necessary to eliminate the personal errors of observation. 
The introduction of the Repsold Transit micrometer has done 
much to eliminate this source of error. 

The effect of all the visible mountain masses on the direction 
of the vertical will be calculated rigorously for the nearer masses, 
and by an approximate graphical process for the more distant. 
In the future it will be considered necessary to examine how far 
these effects are compensated by isostasy. 

Geodetic bases. 

In the chapter on topographical survey we have dealt with 
the use of invar wires in the field, for the measurement of bases. 
We will mention now some of the refinements that are necessary 
when the work is to be of the highest precision. 

At the headquarters of an important geodetic survey provision 
will be made for the standardisation of the wires, to ensure a 
more complete control than is possible when they are merely 
returned to some far distant laboratory at intervals. 

First it is necessary to provide a standard bar, which should 
be the unit of length, yard or metre, multiplied by some power 
■of two, so that it can be compared by successive duplication. 
Four metres or four yards will be the most convenient length. 
But in fact, ten feet has been the usual length of English bars, 
though this involves an awkward comparison with the British 
standard yard. It is not quite clear why, when the yard is the 
standard unit of length, geodetic measurements have been made 
in feet. The modern bar will be made of invar. It will be 
compared with the standard metre at the International Bureau 
of Weights and Measures at Breteuil, or with the standard yard 
at the Board of Trade Standards Office, or with the copies of 
this standard at the National Physical Laboratory or at the 



1 86 GEODETIC SURVEY 

Ordnance Survey Office, Southampton. At the same time the 
laws of its expansion will be minutely studied. 

To avoid duplication of statement we shall speak of the 
operations in future as conducted in metres. India has recently 
decided to make the change, and it is probable that the yard and 
the foot will gradually disappear from geodesy. 

The next step is to establish a 24-metre comparator at head- 
quarters, standardised from time to time with the 4-metre bar. 
This comparator will be in the form of a wall, preferably under- 
ground to escape temperature changes as much as possible. It 
will be provided with tanks in which water can be circulated, to 
allow for the study of the temperature coefficients of the wires. 
On this comparator the wires will be standardised before they 
go into the field, and when they return. 

The constancy of the wires depends very much upon the care 
with which they are treated in the field. They must always be 
wound upon the special aluminium drums which are made for 
them, and they must be treated as instruments of precision 
should be treated, not after the fashion of coils of wire. One of 
the principal difficulties in the field has been to ensure continuous 
careful treatment for the wires, and it has sometimes been 
suggested that if they cost 3000 francs each instead of 30 they 
would be treated with more respect. 

When they are first manufactured they are subject to 
molecular changes and their lengths are not constant. As they 
become aged they settle down into stability, and the process 
may be quickened to some extent by successive very careful 
annealing. But it does not seem that anything can complete 
the natural process of ageing except use in the field. 

It is essential that the coefficient of expansion should be 
found for each separate wire. At first it was the practice to test 
a sample of the rolling from one ingot, and to assume that all 
the batch had the same constants. It is now recognised that 
this is not safe and that each wire must be examined after it 
has been made up into its working form. 

There is still some difference of opinion as to the relative 
merits of wires and tapes. The advantage of wire is that it is 
less subject to the disturbing influence of wind. Tapes have 



GEODETIC SURVEY 187 

several advantages ; twist can be detected very easily ; they are 
not so liable to kink ; and the small divided scale can be engraved 
on the tape itself, instead of on a soldered attachment, the 
" reglette." The last is of considerable importance. 

Experience of their use in rough country has shown that the 
wires or tapes can be used on much greater slopes than was 
considered desirable when they were first introduced. But this 
requires that the provision for determining the slope of the tape 
shall be more thorough than was made in the first patterns. 
Recent experience on the Semliki base in Uganda, and on the 
Lossiemouth base in Elgin, favours the use of an ordinary Y 
level, and a special light levelling staff which can be stood on 
the tripods carrying the fiducial marks against which the tape is 
read. With this equipment it is possible to measure up slopes 
of I in 3, and to choose for the ends of the base situations which 
provide a good view of surrounding stations favourable for the 
base extension. 

This involves a thorough discussion of the effect of slope on 
the horizontal distance between the end marks of the tape, 
arising from the change in the form of the catenary, and from 
the difference of tension at the upper and lower ends — a differ- 
ence which may become so considerable that the pulleys must 
no longer be frictionless, or the tape will run away down hill. 
A very complete investigation of the problem has been made by 
Professor Henrici and his son Captain Henrici, R.E. ; the results 
are too complex for summarisation here. See Ordnance Survey: 
Professional Papers. New Series. No. i. 

For rapid work it is essential that the base party shall be 
well drilled. With a well-trained party a base of 10 km. can be 
measured completely in 12 days; and it is good economy to 
arrange that all the bases required for the whole triangulation 
shall be measured consecutively in a single season if possible. 

Geodetic levelling. 

The immediate practical importance of the main lines of 
precise or geodetic levelling is to provide a foundation for all 
the subsidiary lines upon which the local determinations of 
height, and the contours, are based. Its ultimate scientific, and 



1 88 GEODETIC SURVEY 

perhaps also practical importance, is to discover whether the 
whole country is gradually rising from the sea, or sinking, or 
tilting ; and at what rate the mountains are growing or becoming 
denuded. 

Within the limits of this book we cannot deal with the 
instrumental precautions which are essential in the conduct of 
precise levelling. The general procedure is quite similar to that 
which we have sketched in Chapter IV, page 95 ; but there are 
many precautions to be taken to avoid the small but cumulative 
effects of temperature, of refraction, and of local deviations of 
the vertical. 

It is now realised that the original net of levelling in Great 
Britain was not observed with sufficient precautions to give an 
ultimate verdict on the above points. In particular the deter- 
mination of mean sea level was not satisfactory. A revision of 
the principal levelling is now in progress ; and great attention is 
being paid to the important question of placing the fundamental 
bench marks on solid rock. 

In India the great earthquake of 1905 provoked a very 
interesting enquiry into the changes in relative heights produced 
by the shock. It was found that the difference of height between 
Dehra Dun and Mussooree had been diminished 5*5 inches, and 
it was at first supposed that Mussooree had subsided by this 
amount. But a revision of the line of levels into the plains 
showed that this was not the case. Mussooree in the Himalaya 
and Saharanpur in the plains were found to be at the same 
relative height after the earthquake as before ; but the inter- 
mediate station of Dehra Dun was higher by five inches both 
with regard to Mussooree and Saharanpur. 

There is great reason to think that this movement was only 
an exaggeration of a movement that is always going on, and 
that the Himalayas are gradually pressing forward and up the 
lower lying ranges to the immediate south of them. For this 
reason several lines of precise levelling have recently been 
carried up into the Himalayas, and these are being connected 
with the older formations to the south. It is hoped that in time 
this work may give information on the rate of growth of the 
mountains. 



Plate XXIII 




I. Banog Mountain: Terminal station of an Indian line of precise levels. 




2. Precise Level: United States Coast and Geodetic Survey pattern. 
recise Levelling^. 



GEODETIC SURVEY 189 

Future progress of geodesy. 

Since four-fifths of the Earth's surface is covered with ocean^ 
over which geodetic operations are in general impossible, it is 
clear that we shall never be able to obtain a complete deter- 
mination of the size and shape of the Earth. We shall be 
compelled to make certain assumptions, as for example that its 
figure is an ellipsoid of revolution or spheroid, or that it is an 
ellipsoid with three unequal axes. Then, taking the measured 
arcs of meridian or of longitude as samples of these figures, we 
can determine the size and the form which fit them best. Any 
determination of the figure of the Earth must rest upon a 
discussion of such a kind ; and the result will be the more 
satisfactory the wider the extent of the Earth's surface repre- 
sented in these "samples." 

At the present time we have the following material available : 

The triangulation of Europe, and its connection with Northern Africa. 
A certain amount of work in Russian Asia. 
India. 

South Africa up to Lake Tanganyika, and short arcs in Uganda and in 
Egypt. 

The United States and a Httle in Canada. 

Spitsbergen. 

The arc of Peru. 

A certain amount in Mexico, ChiU, and in Japan. 

The most important work of the future is evidently 

The connection of India with Russian Asia, and the extension of the 
meridian arc to the Arctic Ocean. 

The extension of the European longitude arc across Russian Asia to the 
Sea of Japan. 

The completion of the African arc, and its junction with the European 
triangulation. 

The extension of the Canadian arcs of meridian to the Arctic Ocean. 

An arc of meridian down the chain of the Andes. 

Meridian and longitude arcs in Australia. 

It will be long before this programme is finished. Mean- 
while we may say a few words on the present state of the 
problem. 



I90 GEODETIC SURVEY 

No recent attempt has been made to bring into discussion 
all the available material. The greater part of modern work 
is discussed with reference to the figures of Bessel and of 
Clarke. 

Bessel's determination was based on the European and 
Indian results available in 1841, and the old measure of the 
arc of Peru. 

Clarke's several determinations of 1858, 1866, and 1878 
depend on considerable extensions of the same material ; they 
take into account the extensions of triangulation in Europe 
and in India, but have nothing to add from other parts of the 
world. 

The recent determination by Hayford is based on the United 
States only. 

At the end of this chapter we give a table of these results. 
It will be seen that the differences between them are not very 
great, and that the contribution of the United States does not 
suggest that the shape of the western hemisphere is very different 
from that of the eastern. 

Bessel, Hayford, and Clarke in one of his solutions, assume 
that the Earth is an ellipsoid of revolution. In a second solution 
(1878) Clarke assumes that the Earth is an ellipsoid not of 
revolution, or that the equator is elliptical. In a third he 
assumes that the Earth is a figure of revolution, but not the 
revolution of an ellipse. He finds that the evidence for the 
second or third of these hypotheses is so slight that they cannot 
be said to lead to any positive result. At present there is no 
real reason for supposing that the equator is not a circle, or the 
meridian an ellipse. 

It would seem that the time has come for a new solution of 
the problem, to take into account all the material which has 
accumulated since Clarke's last solution was made. But the 
necessity of including a discussion of isostasy and compensation 
very much increases the labour. 



GEODETIC SURVEY 



191 



Figure of the Earth. 

The following table gives the results of the principal dis- 
cussions of the dimensions of the spheroid : 





Equatorial 
Semi-diameter 


Flattening 


Polar 
Semi-diameter 


Bessel 1841 
Clarke 1866 
Clarke 1880 
Hayford 1910 


6377397 m. 
6378206 
6378249 
6378388 


l/299'2 
1/295-0 
1/293-5 . 
1/297-0 


6356079 m. 
6356584 
6356515 
6356909 



From a general discussion of pendulum observations Helmert; finds (1901) 
for the flattening 1/298-3. 

Bessel's results were based on the various triangulations of Europe 
executed at that date. 

Clarke's 1866 figure included the French, British, Indian, Russian, South 
African, and Peruvian arcs so far as they were then complete. 

Hayford's figure depends entirely on the geodetic arcs of the United 
States, and includes an elaborate discussion of isostasy. 

With Clarke's figure of 1880 the quadrant of the meridian is 10,001,868 
metres, so that the metre is shorter by about one part in five thousand than 
the ten millionth of the quadrant. 



CHAPTER VIII 

SURVEY INSTRUMENTS 

This book is not intended to supply the place of a technical 
handbook in which all the details of the instruments, the methods 
of adjustment, and of observation, are given minutely. Such 
information may be found in full in the Textbook of Topographical 
Surveying, to which reference is made so often, or in other 
technical works. But it will be well to give here a few notes to 
supplement the slight accounts of the various instruments given 
throughout the book. 

The Sextant. 

The sextant is pre-eminently a sea instrument, and it is not 
well adapted for use upon land, except under special circum- 
stances. 

The sextant will measure angles up to about 130° but not 
more. Held in the hand, it can be adjusted to allow for the 
motion of the ship in a way that becomes for the skilled observer 
almost automatic. It fulfils all the needs of the sailor, who 
measures elevations above the visible sea horizon, and occasion- 
ally angles between the moon and the sun or a star, for the 
almost obsolete method of lunar distances. It gives results 
which are nominally correct to \d' and actually correct to 
within half a minute of arc, which is just the degree of accuracy 
required in navigation. The principal systematic error to which 
the instrument is liable is theerror of eccentricity of the graduated 
arc — the error which in the theodolite and other more precise 
instruments is eliminated by reading the circle at two opposite 
points, which is impossible in the sextant. 

It is the possibility of this error developing undetected that 



SURVEY INSTRUMENTS 193 

makes it waste labour to equip a sextant with a stand, as has 
been done, and to try to make use of it upon land. 

On land the sextant cannot give altitudes directly, because 
there is no visible sea horizon from which to measure. It is 
necessary to employ what is somewhat confusingly termed the 
" artificial horizon " : a dish of mercury which forms a naturally 
level reflecting surface, or a reflector of blackened glass which 
can be set level by levelling screws and a bubble. The sextant 
then measures the angle between the direct and the reflected 
images of the sun or star, that is to say, double the altitude of 
the body. But angles greater than 130° cannot be measured. 
Hence when the sun at noon is higher than about 65°, which 
is very frequent in tropical and subtropical regions, the noon 
altitude of the sun cannot be taken on land with a sextant. 
This serious limitation is enough to condemn the use of the 
instrument on shore. Moreover, the sextant cannot measure 
azimuths except in a roundabout way, which involves a great 
deal of observation and unnecessary calculation. 

If, then, it is necessary to retain the sextant as a subsidiary 
instrument for work on land, its use should be restricted to those 
cases in which it must be employed for reasons of secrecy. 
There are native tribes which would interfere with a surveyor 
working at an instrument mounted on a tripod who would not 
be so likely to notice a man lying down on his face taking sights 
with a sextant. It is said that native Indian surveyors have 
done good work in trans-frontier regions with a sextant disguised 
as a praying wheel. 

The sextant has often been employed on polar expeditions, 
on account of its small size and lightness. The observation of 
such small altitudes as the Sun has in spring in polar regions 
offers, however, peculiar difficulties when an artificial horizon 
must be employed ; and it is now generally admitted that a 
small mountain theodolite should always be employed on such 
work. It has the great advantages that its errors are self- 
eliminating, and that it can be used with facility to measure 
azimuths. A modern mountain theodolite of the smallest size 
weighs no more than a sextant with artificial horizon, and the 
results that it gives are far more satisfactory. 

H. M. s. 13 



194 SURVEY INSTRUMENTS 

The theodolite. 

For many years the ordinary surveyor's theodolite suffered 
from a want of intelligence in its design, of which traces still 
survive in the patterns manufactured especially for engineers. 
The most conspicuous of these is the four screw levelling device, 
which inevitably strains the instrument, makes the screws work 
loose, is thoroughly bad in design, but is still very often made. 

The old-fashioned theodolite was effective only for horizontal 
angles, in which reversal is not much required. When it was 
found to be advantageous to make the instrument reversible, 
which requires that the telescope shall be able to pass through 
the frame, the new pattern was called on this account a " transit 
theodolite," which name still survives in the makers' catalogues : 
a stupid name which suggests that the theodolite can be used as 
a transit instrument. 

The circles of the old-fashioned theodolite were read by 
verniers only, and verniers are awkward to read by day, almost 
impossible to illuminate properly for reading at night. The 
greatest modern improvement in theodolites has been the 
application of the micrometer microscope, which increases the 
accuracy of reading the circle at least fivefold, and at the same 
time makes it much more simple and easy : a very unusual 
accompaniment of gain in precision. The five inch micrometer 
theodolite has now established itself as the standard instrument 
for survey of the second order, that is to say, in which geodetic 
accuracy is not required. The instrument is sufficiently portable 
for the employment upon boundary survey under the roughest 
conditions ; and the facility with which it can be used for field 
astronomy makes it invaluable both in teaching and in actual 
use in the field. (See Plate XX.) 

The modern theodolite is especially adapted for the accurate 
measurement of vertical angles, in which the old instruments were 
very deficient The improvements in construction which have 
led to this result are two : making the instrument reversible, 
already mentioned; and the' mounting of a sensitive bubble upon 
the frame which carries the verniers or microscopes for reading 
the vertical circle. Since there is often some misconception as 



SURVEY INSTRUMENTS 195 

to the part played by these two devices, we may examine them 
shortly. 

It must be remembered that there is a great difference 
between the measurement of horizontal and of vertical angles : 
the former are relative, the latter are absolute determinations. 
Or in other words, on the horizontal circle one measures the 
difference in bearing between one point and another ; on the 
vertical circle one measures the elevation of a point above 
the horizon, which is not a visible object on which settings can 
be made, but must be defined by means of sensitive levels or 
bubbles mounted on the instrument. To measure an absolute 
elevation naturally demands that all the effects of errors of 
adjustment, collimation, zeros of microscopes, and so on, shall 
be eliminated ; and this can be secured by rev^ersing the 
instrument about a stable axis very nearly vertical. If the 
approximately vertical axis of the theodolite could be trusted to 
remain fixed during the series of settings and reversals of the 
instrument which take place in the course of a series of obser- 
vations on an object, or even to remain fixed for the pair of 
observations, " face left and face right," which constitute a 
complete observation, then the reversal would eliminate all these 
errors of collimation and zero automatically, and nothing more 
would be required. But in practice the foundation of the 
instrument is not perfectly stable. Under the influence of the 
movements of the observer and the weight of the instrument 
itself, slight settling takes place between one setting and the 
next ; and perhaps also the position of the microscopes on the 
frame changes a little by reason of change in the temperature. 
It is the function of the bubble mounted on the microscope arms 
to eliminate these changes, and the introduction of this device 
has very much increased the accuracy of the results. 

When the errors of the instrument are eliminated there 
remain the personal errors of the observer ; and these also can 
be eliminated in great part by a proper use of the principle of 
reversal. An observer will have a tendency, quite unknown to 
him, and almost ineradicable, to make settings systematically 
high or low. This is called the personal error of bisection. It 

13 — 2 



196 SURVEY INSTRUMENTS 

may be eliminated by combining observations in which the error 
comes in with opposite effects upon the quantity which is to be 
determined. Observations made north and south of the zenith 
will be affected with the same error in altitude, but this will 
produce opposite errors in the resulting latitude. Similarly the 
personal errors in observations made east and west will have 
opposite effects upon determinations of time. Thus by preserving 
a balance between north and south or east and west stars the 
consequences of these errors will be eliminated in the mean. 

Formerly the astronomical observations for latitude were made 
with a special instrument, the zenith telescope (see Plate XXII). 
Modern geodetic theodolites are now fitted with the necessary 
micrometer eyepieces, so that observations for latitude by Tal- 
cott's method may be made with them, and the zenith telescope 
is becoming obsolete. 

Levels. 

Very great improvements have been made in the construction 
of precise levelling instruments during recent years. In the 
older instruments it was necessary first to adjust the foot screws 
so that the bubble was in the centre of its run, and then to walk 
round to the eyepiece and make the reading on the staff. In the 
meanwhile the bubble had probably shifted. In the modern 
level it is possible to see both ends of the bubble by a second 
telescope fitted alongside the principal, and read with the other 
eye. The final adjustment of the bubble is thus made imme- 
diately before reading the staff, and without changing position. 
Further, all the essential parts of the instrument are constructed 
of invar, so that the effects of temperature are almost eliminated. 

Three parallel horizontal wires are fitted, and the staff is read 
against all three. This helps to eliminate accidental errors of 
reading, and also provides, on the principle of the tacheometer, 
for the control of the equality of the distances between the 
forward and the back staves. 

The staves are graduated on both faces, the second graduation 
being from an arbitrary zero, so that the second set of readings 
is not a close repetition of the figures of the first. And special 



Plate XXIV 





I. Strainine" trestle. 



2. Tape on drum. 





3. Mark on tripod. 



4. Alignment sight on tripod. 



Invar Tape Base Apparatus. 



Department of Geography, 
Cambridge University. 



SURVEY INSTRUMENTS 197 

precautions are taken to control at frequent intervals the lengths 
and the graduation of the staves. 

Invar tape or wire base apparatus. 

As a result of experience in the field certain modifications 
have been made in the apparatus as it was designed by M. 
Guillaume at the International Bureau at Breteuil. We have 
already mentioned the improvement in the levelling arrange- 
ments, which make it possible to measure up slopes as great as 
one in three. The straining trestles and the mark tripod have 
also been improved. The apparatus which we illustrate was 
designed at Cambridge, after learning the experience of measure- 
ment on the Lossiemouth and Semliki bases. It was made in 
the Observatory workshop, largely by the skill of Mr Gordon 
Dobson, B.A., of Gonville and Caius College. (Plate XXIV.) 

The straining trestle has, as is now usual, one leg prolonged 
to rest on the shoulder of the operator, so that he can take the 
weight of the wire while he adjusts the other two legs. The 
novel feature of the design is the swivelling hinge of these legs, 
so that the tripod is capable of some lateral motion without 
taking the points of the legs from the ground. This is very 
convenient in adjusting the wire to the line of the tripod marks. 

For convenience and rapidity of work it is essential that the 
tripod mark should be adjustable over a range of a foot without 
moving the tripod itself; for on rough ground it is not possible 
to set the tripod up level at any exact point desired, nor to 
move it readily by small amounts. The head of the Cambridge 
form of tripod is a skeleton triangle ; and the post for the mark 
is carried through two battens, one above and the other below 
the triangle. A wing nut at the base of the post tightens the 
two battens and holds them, or allows a range of motion and 
possibility of clamping at any point over a circle of about a foot 
in diameter. 

Longitudes by telegraph. 

When two stations are connected by a land line it is easy to 
arrange for an exchange of time signals, for the determination 
of the difference of longitude of the stations. 



198 SURVEY INSTRUMENTS 

The arrangements usually described for this purpose, with a 
clock and one or more chronographs in circuit with the signal 
keys of the observers at the transit instruments, are excellent 
when the distance is not too great, and the line is in the best 
condition. When, as often happens in tropical countries, the 
insulation of the line is poor, and it is not possible to send 
enough current to operate sounders or chronograph pens, it is 
possible to get quite good results with the telephone " buzzer." 
The technical difficulties are naturally much increased when a 
submarine cable is interposed in the connection between the two 
stations. It would be out of place here to describe the details 
of the operations. But whatever the instrumental arrangements, 
the principle of the method must remain the same. In its 
simplest form it is as follows. 

The observers at each station determine their local time with 
transit instrument or theodolite ; that is to say, they determine 
the errors of their chronometers on those times. At agreed 
instants each sends to the other a series of signals in beat with 
his chronometer. Thus there is a double comparison between 
the chronometers at the two stations ; and the error of each 
being determined, there is a double determination of the differ- 
ence of longitude. 

The accuracy of the comparison is increased if one of the 
chronometers keeps sidereal, and one mean solar time. To 
eliminate the personal equation of the observers it is usual to 
exchange stations ; but this is not always efficacious, and it is 
better, if possible, to adopt the transit instrument with the 
moving wire, by which the personality of the observer is very 
much reduced. 

So long as telegraphic longitudes depended upon the main- 
tenance of long land connections, or on the courtesy of the 
Cable Companies, the opportunities for longitude work were 
necessarily limited. But the recent rapid development of Wire- 
less has entirely altered the conditions of the problem. 

Longitudes by wireless. 

In the year 1910 thQ Bureau des Longitudes of Paris organised 
a service of time signals from the military wireless post of the 



I 



SURVEY INSTRUMENTS 199 

Eiffel Tower, in co-operation with the Paris Observatory. Twice 
in the 24 hours they send out a series of signals which can be 
received all over the Eastern Atlantic and Mediterranean, and as 
far south as Dakar and Lake Chad. A well equipped survey 
party can carry the necessary receiving apparatus without much 
difficulty, and transmitting apparatus is not needed. It has 
thus become possible to determine longitudes with facility, which 
will have a great effect upon the methods of survey in northern 
Africa. Triangulation in the Sahara is difficult and costly, 
owing to the great distances over which supplies must be 
carried. It seems probable that in country such as this triangu- 
lation will be superseded by determinations of latitude, and of 
longitude by wireless. Owing to local deviations of the vertical 
the results will not be so consistent as those of triangulation, but 
they will have the great advantage that they can be obtained in 
country which is almost impracticable for any other method ; 
and especially they will facilitate the rapid mapping of country 
which is too poor to afford triangulation. 

At the time of writing arrangements are in progress for 
a great improvement in the accuracy of these wireless time 
signals, and for a world wide extension of their range. At a 
conference held in Paris in October 191 2, at the instigation of the 
Bureau des Longitudes, it was resolved to create an international 
organisation, which will receive from a great number of Observa- 
tories their deduced corrections to the wireless time signals, 
which will be utilised in correcting the subsequent signals. By 
this means it will be possible to ensure that, however bad the 
weather may be in Paris, and however long it may be since the 
Paris Observatory obtained star observations, the combined 
resources of European observatories will supply the time correct 
to within a few hundredths of a second. 

The time of transmission of the wireless signal is infinitesimal, 
so that any observer within range of the Eiffel Tower, whether 
on land or sea, will be able to determine his longitude with 
a precision hitherto quite impossible. It will be interesting to 
see how far it will be practicable to eliminate errors in retrans- 
mitting the signals from station to station round the world. 



200 SURVEY INSTRUMENTS 

Geodetic pendulums. 

The form of apparatus now in general use is due to Major- 
General von Sterneck. It consists of a set of several small 
pendulums adjusted to swing in very slightly more than half 
a second. The pendulums are made of brass, heavily gilded to 
avoid change by corrosion. They rest by delicate agate knife 
edges on an agate plane carried by the stand. Each pendulum 
carries a small vertical mirror on its head, just above the line 
of the knife edges. There is an arrangement for giving the 
pendulums a small displacement and then allowing them to 
swing freely ; the arc of vibration is less than half a degree. 
They are set swinging and gradually come to rest. 

A dummy pendulum similar to the others contains a 
thermometer, to determine the temperature of the pendulums. 
The stand is massive ; but it is not possible to consider it as 
perfectly free from flexure and vibration. There is therefore 
a special arrangement attached to the stand to enable the 
correction for flexure to be determined. The principle of this 
determination is elegant. If two pendulums hang side by side 
and one is set swinging, while the other is initially at rest, 
the latter will gradually take up the oscillations of the former, 
unless the stand is perfectly rigid. The flexure of the stand 
is thus determined from the rate at which the first pendulum 
influences the second. 

The periods of vibration of the pendulums are found by 
comparing them with the beats of a half-seconds clock, which 
is rated by star transits. Each half-second the clock momen- 
tarily opens the shutter before the slit of the " flash-box," and 
the illuminated slit is reflected in the vertical mirror on the 
pendulum, and viewed in a small telescope on top of the 
flash-box. (Plate XXII.) 

Thus a line of light is seen in the field of the telescope 
every half-second ; and, as the clock gradually gains on the 
pendulum, the position of the line moves down in the field, 
and the time when it coincides with a central horizontal wire 
can be determined. The interval between one coincidence and 
the next is the interval in which the pendulum loses one swing 



SURVEY INSTRUMENTS 201 

on the clock. The observations being continued over a period 
of several hours, the comparison between the clock and the 
pendulum becomes of great precision, with a probable error of 
only three or four parts in ten million. 

This apparatus is fairly portable, and the necessary observa- 
tions for the determination of the value of gravity at a single 
station may be made in a couple of periods of three or four 
hours, generally chosen so that one is at night and one by day. 
But it takes several days to get the clock properly rated by star 
transits ; and thus in the past the greater part of the time at 
each station has been spent in determining time and rating the 
clock. It seems likely that in the future much time will be 
saved by using the wireless time signals to rate the clock. 



INDEX 



Adjustment of traverse 126 

of triangulation 158 

Aero-maps 56 

Africa, British : Survey of 168 

: arc of meridian 181 

Airy : attraction of mountains 1 74 

Amsler planimeter 34 

Aneroid barometer : use of 76 

Angot : barometer heights 79 

Arc of meridian 171 

: geodetic measure 179 

: principal determinations 181 

Areas : measurement of 33 

Artificial horizon 193 

Astronomical observations : route traverse 
60, 67 

navigation 60 
with compass sketch 10 1 
topographical survey 141 
geodetic survey 171, 184 

Attraction of mountains 173 

Australia : Survey of 167 

Austria- Hungary : school maps 48 

Austrian General Staff: map of Central 
Europe 47 

Azimuth : determination of 60, 69, 143 

: initial 141 

: reverse 159 

Baily : barometer heights 77 
Barometer heights 74 

: theory 77 

: tables 80 

Barometer: relation with level of sea 134 
Base in simple theodolite survey 90 

: for compass sketch 106 

: for plane table sketch 114 

: for topographical survey 144 

, : correction for slope 147 

: reduction to sea level 148 

: closing one on another 159 

: for geodetic survey 185 

: Cambridge apparatus 197 

Bavaria : analysis of select maps 45 

Beacons 137 

: self-centering 140 



Bench marks 23, 188 

Bessel : figure of the Earth 190 

Boiling point thermometer 80 

Boundary surveys 169 

Breteuil : Bureau des poids et mesures, 

standardisation of wires 145 

: of bars 185 

Bureau des Longitudes : wireless time 

signals 198 

Canada: Survey of 167 

: map published by British General 

Staff 41 

Cassini : arc of meridian 181 

Chain survey 84 

Chains of triangulation 184 

Characteristic sheet 5, 127 

Chatham, School of Military Engineering 
vii, 128 

Chronometers 67 

Clarke: form of ocean surface 178 

: figure of the Earth 179, 180 

Clinometer, Indian loi 

: description 161 

Clinometer, Watkin loi 

: adjustment 109 

Close viii 

: Textbook of topographical survey- 
ing V 

field printing company 36, 77 

theodolite triangulation 149 

trigonometrical heights 155 

Survey tables 159 

instrumental adjustments 192 

Close-Brooker alidade 128 

Colonial Survey Committee : Report 83, 
168, 169 

: work of 1 68 

Comparator for wires 186 
Compass, prismatic 65, loi 

: deviation of 69, 70 

: local deflections 104 

: plotting bearings 105 

: use of 102 

Compass, trough 113, 120, 124 
Compass sketching loi, 105, 107 



204 



INDEX 



Compass-traverse 6i, 62 

check by latitude and azimuth 

71 

cannot make map 72 

Compensation of mountain attraction 

174, 176 
Contours 23 

with clinometer iii 

with level and chain 165 

Conventional signs 5, 29, 127 
Cross-bearings 64 

Curvature of Earth : in levelling 98 

: in plane-tabling 128 

: in triangulation 92, 152 

Cyclometer 62 

Dead-reckoning 6i, 71 
Dehra Dun: gravity at 177 

: change of height 188 

Diplomacy : importance of maps in 4 
Distances : measurement on map 34 

: by time 63 

Dobson: base apparatus 197 

Durand : reconnaissance ladder ix, 135 

Dutton : isostasy 177 

Egypt, Survey department vii 

: self-centering beacons 141, 183 

: horizontal refraction in Nile valley 

152 

: triangulation up the Nile 137 

: arc of meridian 182 

Eiffel Tower: time signals 199 
Exploratory survey: methods 130 

Faye : gravity on islands 176 
Ferrero : report on triangulations 182 
Field book of compass traverse 64 
Figure of the Earth : method of finding 
171, 180 

: basis of Survey tables 159 

: present knowledge of 190 

Fisher : Physics of the Earth's Crust [74 

Forest : Survey of 73 

Form-lines 23 

France : analysis of select maps 44 

General Staff : Geographical Section 41 

: analysis of select maps 42 

: map of Africa 73 

: map of Canada 167 

Geodesy vi 

: definition 171 

: figure of Earth 179 

: principal arcs 181 

: future progress of 189 

Geographical positions from triangulation 

158 
Gill : use of geodetic survey 94 
: geodetic survey of S. Africa 183 



Graticule : construction 160 
Gravity: local deviations 142, 143 

: in geodesy 172 

: pendulum survey 176 

Great Britain : see Ordnance Survey 
Greece : analysis of select map 48 
Greenwich time 68 
Guillaume : invar base apparatus 197 



[90 



Hachures 20 

Hayford : figure of the Earth 

Hecker : gravity at sea 176 

Hedley viii 

Heights: by barometer 74, 77, 80, 156 

: by clinometer 127 

: by theodolite 153 

: datum no 

Heliograph 138 

Helmert : flattening of the Earth 191 

Henrici : theory of base measures 187 

Hill features : representation of 19 

Hill paths, failure to show 8 

Hill-shading 2 1 

Himalayas, attraction of 173 

: partial compensation of 177 

: effect on form of ocean surface 178 

: levelling in the 188 

Hypsometer, or boiling point thermometer 

80 
Hypsometric tints 27 

Identification of objects 33 
India, Survey of vii, 167 

: Survey tables 77, 159 

: gravity in 173, 176 

International Geodetic Association vii 
International Map 5 

: history of 50 

: analysis of select sheets 54 

: conventional signs : roads 8 

: railways 10 

: rivers 16 

: woods 17 

Intersected points 107, 
Intervisibility of points 
Invar wires 145, 

bars 185 

Isostasy 177 

Italy : analysis of select maps 47 

Jack ; beacons on the Uganda-Congo 
boundary ix, 139 

Kew, base station for gravity survey 177 

Lallemand : projection for international 

map 52 
Lamps for beacons 138 
Land Survey 83 
Laplace: barometer heights 77 



119 

197 



INDEX 



205 



Lapland : arc of meridian 181 
Latitude : determination of 60, 67, 142, 
196 

: initial 141 

: local deviations 1 74 

Latitude and departure tables 71 
Layer colouring 27 

on international map 55 

Level 95, 96, 196 
Levelling 93 

of precision in Great Britain 166, 

188 

connection between tide gauge and 

triangulation 134 

geodetic 187 

Levelling staves 95 

Longitude : determination of 60, 67, 
J42 

: by telegraph 68, 197 

: by wireless 198 

:»initial 141 

Looniis : barometer heights 77 

Lossiemouth base 187 

Lunar distances 68 

Lyons : Cadastral Survey of Egypt vii 

Magnetic meridian : shown on O. S. maps 

: on plane table 1 20 

: on compass sketch 105 

Manual of Map Reading (Official) v 

conventional signs 6 

Map reading 30 

Maps, Cadastral : definition 2 

: Ordnance Survey 38 

: triangulation for 162 

: necessity for 2 

: topographical : definition 2 

Margins of sheets 17 

: international map 55 

Meridians on O. S. maps 19 

Metric system 51 

Military works 30 

Morris : geodetic triangulation of South 

Africa 183 
Mount Everest : discovery of height 156 
Mountains, attraction of 174 

Names : transliteration on maps 55 
Natal : want of maps 3 
National Physical Laboratory : standard- 
isation of wires 145 

: bars 185 

: thermometers 82 

Natural scales 1 1 

Navigation : astronomical observations 60 



analysis of select sheets 
36 



24 



Ordnance Maps : 

38 

: methods of reproduction 

Ordnance Survey vii 

: conventional signs 5 

: roads 6 

: railways 9 

: rivers 15 

: woods 1 7 

: contours 24 

: other signs 29 

: rule for figuring contours 

: accuracy of principal triangulation 

182 

: history 163 

: present state and plans for future 

165 

: principal stations 140, 164 

: cost 166 

Paris Observatory : time signal 199 

Patchwork survey 95, 132 

Pencils ro2 

Penck: proposal for International Map 50 

Pendulum-survey 175 

Perambulator 62 

Personality in observation 195 

Peru : arc of meridian 181 

Picard : arc of meridian 181 

Plane table and accessories 113,125, 127 

: graphical use of 114, 128 

: accuracy of 118 

: resection 121 

: traverse 125 

: triangle of error 122 

: failure of solution 124 

Planimeter 34 

Poles, determination of position near 62 

Pratt: attraction of Himalayas 174 

Profiles 31 

Projections, Map 34, 160 

Protractor loi, 105 

: scales on 14, 112 

Quadrilateral chains 136, 184 



Occultations 68 
Ocean surface, form of 
Ordnance Maps 37 



178 



Railways, representation of 9 
Reconnaissance: plane table 118, 
Reconnaissance-ladder 135 
Rectangular coordinates of triangulation 

159 
Refraction : in levelling 98 

: in trigonometrical heights 

: of horizontal angles 152 

Representative fraction it, 13 
Reproduction of maps 35 

: in the field 36 

Repsold transit micrometer 185 
Resection by compass 108 
by plane table 121 



135 



153 



2o6 



INDEX 



Rivers : representation of 15 

Roads : representation of 6 ; and see 

Map Analysis, Chap. 11 
Route map 59 
Roy : first director of Ordnance Survey 

163 

: triangulation of England 181 

Ruling points 107 

Salisbury Plain base 164 
Saxony: analysis of select map 45 
Scale of maps 10 
Scales, construction of 13 

natural 1 1 

Sea-level: determination 133 

: reduction of triangulation to 148 

: revision of British datum 166 

Sections 30, 98 
Semliki base 187 
Sextant 192 
Sight-rule 113 
Signals: luminous 138 

: opaque 139 

Sketch : definition 100 
Sketching detail 108 
Snellius : measurement of arc 181 
South Africa : Survey of vii, 168 
Southern Nigeria : barometer heights 76, 
156 

: precise traverse 162 

Spherical excess 152 
Spitsbergen : arc of meridian 181 
Spot-heights 23 

: by Indian clinometer r6i 

Standardisation: of base bars 185 

: thermometers 82 

• : wires 145 

Station-marks 140 

Struve : European arc of meridian 181 

Subtense methods 129 

Survey : cadastral 2 

: topographical i, 132 

: geodetic 171 

Sweden : analysis of select maps 49 
Switzerland : analysis of select maps 46 



1S4, 196 
145 



149 
195 



194 



Tacheometer 129, 196 
Talcott's method for latitudes 
Tapes for base-measurement 
Theodolite: geodetic 183 

: mountain 193 

: triangulation 88, 91 

: method of observation 

: horizontal angles 149, 

: vertical angles 153 

: instrumental adjustments 

: micrometer 194 

Tide gauge 133 
Time signals 199 
Topographical survey i, 132 
Traverse : precise 73, 162 

: compass 6r, 62, 71, 72 

: compass checked by astronomical 

observation 67 

: plane table 125 

: adjustment of 126 

Traverse tables 71 

Triangle of error, in plane tabling 122 
Triangular error 151, 184 
. Triangulation 88, 92 

: with compass 107 

: with plane table 116 

: use and accuracy of graphical 118 

: with theodolite 136, 149 

: computation 156 

: geodetic 183 

Trigonometrical heights 153 

: accuracy 155 

Trough compass 113, 120, 124 

Uganda-Congo boundary 4 

United States : analysis of select map 50 

: geodetic survey 178, 190 

War Office, Geographical Section 41 
Wilson : Topographical Surveying 147 
Wireless telegraphy 68, 185, 198 
Wires for base measurement 145 
Woods and forests: representation of 17 

Zenith telescope 196 



CAMBRIDGE: PRINTED BY JOHN CLAY, M.A. AT THE UNIVERSITY PRESS. 



^Y THE SAME AUTHOR 

Map Projections 

By Arthur R. Hinks, M.A., F.R.S., Chief Assistant, Cambridge 

Observatory, and University Lecturer in Surveying and Cartography 

Demy 8vo. pp. xii+ 126. With a frontispiece and 19 figures 

Price ^s. 7iet 

Press Notices 

"Notwithstanding the large amount of surveying which has been done in this 
country and throughout the Empire, there are few works in Enghsh which treat of the 
various ways in which portions of the earth's surface may be most conveniently and 
correctly represented on the plane surface of a map. The subject has been treated 
partially by several eminent mathematicians, and valuable summaries occur in some 
encyclopaedias, but we do not in this country possess any works such as those by 
Germain, Tissot, Hammer, and others. There are also many works of a less 
advanced type which are available to Continental geographers, but this class, too, is 
very insufficiently represented here. We therefore welcome the appearance of the 
present volume, in which the subject is treated clearly and in a manner which makes 
but small demand upon the mathematical training of the geographer, while at the 
same time the important points in any projection, suitability for special purposes, and 
facility of construction are given especial prominence. After indicating the inevitable 
limitations of all projections, in representing length, area, and shape of any portion of 

the earth's surface, the author reviews the principal systems Conical, cylindrical 

and zenithal, as well as certain conventional projections, are well described and 
clearly explained, their special advantages and points of weakness being indicated. 
A chapter on the projections in actual use is an instructive addition. The chapter on 
the simple mathematics of projections treats of the theory of each particular case, and 

discusses the errors which may arise in its use under different conditions The present 

volume will be of great use to all geographers, and should pave the way for a more 
serious study of cartography on scientific lines than yet generally obtains. Great care 
and labour are expended on the measurements of various regions in order to produce 
trustworthy surveys, and the utilisation of the results should be based on sound carto- 
graphical principles, and in such a work this book will be a valuable assistance." 

Nature 

" Writers who have dealt with the matter in the past have, as a rule, been 
mathematicians who, after elaborate investigations, have arrived at conclusions, 
frequently expressed in lengthy formulae, which the ordinary man who has to 
construct maps fails to follow ; or they have been those who have gone to the other 
extreme, and seeking to free the subject from supposed complications, have left out 
most of the mathematics, and produced books which, though giving diagrams and 
more or less approximate rules, fail entirely to satisfy students desirous of following 
the subject intelligently. The sort of book that was for a long time almost entirely 
wanting for the ordinary geographer and map draughtsman was a mean between these 
two. Mr Hinks, who is well known as an astronomer, has now taken up the subject, 
and while he fully admits his indebtedness to Colonel Close and others, has produced 
a work of considerable interest, which should go a long way towards meeting this 
need, and one which possesses decided originality as regards some of its subject- 
matter and method of treatment.... The Introduction is specially good, and the 
explanations, both in this and other sections of the book, are illustrated by small 

diagrams that must be of great assistance in making matters clear A specially 

interesting chapter is that on the Errors of Projections. Some six to nine different 
projections are dealt with and the results are not only interesting, but will be of 
considerable value to those engaged in map drawing." — Geographical Journal 

Cambridge University Press 
Fetter Lane, London. C. F. Clay, Manager 



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